I will chime in here. She is not an empath. Her displays of empathy are "cognitive empathy", logically derived to appear empathetic rather than genuine emotionally based empathy. Her apology is "false contrition" utilized to keep you in the relationship for what you provide her. I say this because when empaths get caught cheating they don't react the way she did and they stop, plus it is rarer for them to cheat, especially blatantly in front of you.
You possibly have a Narcissist on your hands. They are very common in the population as a whole (1 out of 6) and even more so in the cuckold and sharing communities because the various interplay of sharing relationships align with the Narcissist's need for control.
I would need additional information to make a more certain determination, but with what you have given us I think the odds of her being a Narcissist are high. The reason I say this is because you are near the end of the first phase of a Narcissistic relationship called the "Golden Period" where they profess your perfection, will tell you things like God sent you to them, they will do anything for you, they like what you like and they give you lots of sex, and they make promises to give you big things you want in the future and life is fantastic with this wonderful person who you can't believe came into your life; it's as if you are in a relationship with your clone, that is how compatible you are with them. Then the problems start as you enter the longest phase of a Narcissistic relationship, "Sustained Devaluation". This is the period where the Narcissist triangulates you by playing you against other men, lies to you, cheats on you, starts backing away from their big promises to you (Future Faking), gaslighting you when they claim to never have said something or done something making you question your own reality, begin withdrawing their affection slowly but noticeably and generally drive you crazy with confusing behavior, statements and actions towards you which you try to make sense of considering how well things were just going.
Welcome to the emotionally painful and confusing Sustained Devaluation of a relationship with a Narcissist. You should know that you will never really get the Golden Period back, but will be bread-crumbed (small periods of respite) then sent back to devaluation. This works on your psyche to create an emotional addiction to the Narcissist. Her intuition is telling her that your ensnarement is good enough, that you are now under sufficient control as a committed partner to begin using corrective statements and actions on you to begin the slow sure process of destroying your self-esteem so that you morph into a more and more easily controlled partner that will serve her.
A big problem for Narcissistic victims is that over time you become "trauma bonded" to them, a "Stockholm Syndrome" type psychological state, which keeps you attached to the Narcissist. The severity of this trauma bond is determined by the victims underlying emotional makeup, the length of time in the relationship and how early in life the relationship began. These then define the difficulty the victim of the Narcissistic relationship will have in escaping from the toxic union.
I personally know a 45 year old man who has been in a relationship with a Narcissist since he was 15, with personality traits putting him at the bottom in terms of ability to break free of his trauma bond (High Empathy Low Self-Esteem), suffering from a mid-life crisis with an alcohol addiction and the Narcissist was implementing a brutal discard of him. My overwhelming convictions is that he will never break the trauma bond he has formed with his Narcissist, which has physically wired his brain (created new physical connections over a long duration) as a consequence of his Narcissist's psychological manipulation. This is literally a life threatening situation for him. Fortunately, due to circumstances the Narcissist picked him back up off the shelf for a respite period, but had things continued as they were I don't believe he would have survived a year. This is not an exaggeration or some kind of hyperbole, these relationships are that destructive to the Narcissist's victims. Often the emotional, mental and even physical abuse of a Narcissist during the discard phase reaches a level that is difficult to capture with words in its cruelty and brutality. Typically this further confuses the victim as they have done nothing differently or wrong; the Narcissist has just found their replacement and is no longer in need of them for now, so they emotionally and sometimes physically torture their victim which makes the Narcissist feel powerful and in control. They actually relish inflicting pain on someone they supposedly loved. It is pretty sick to experience or witness, but it is the reality of these evil people.
My own personal experience with cognitive (phony) empathy illustrates a Narcissist's fake façade versus the real person. I was with a Narcissist woman recently for 5 days. Great looking 30 year old who everybody thought was a sweet, kind, and caring person who didn't have a mean bone in her body. I know how to draw out Covert Narcissists to expose themselves from experience. It is a self protection skill I developed to identify them quickly because I definitely attract them. This girl went fucking stupid psycho when I used my Narc test on her. Your girl's appearing to be highly empathetic as you say could actually be a manipulation technique she uses to ensnare and fool people. Narcissists are different people with their intimate partners behind closed doors where their abusive behavior (verbal and/or physical) can't be seen by "their public", hence everyone is shocked when they are unmasked due to some event which shows the real person. Their abusive behavior usually gets into full swing about 6-12 months into the Sustained Devaluation phase of the relationship. During this timeframe the victim will seek to appease the Narcissist in the hope of returning to that amazing Golden Period, but except for short periods of bread-crumbing respite, they will never get back there.
Most Narcissists, especially females of their kind, create a false persona to present to the outside world of colleagues, acquaintances, friends, etc. This fabricated façade is constructed as a protective mechanism to shield their feelings of inadequacy and low self-esteem from the outside world. They are constantly in need of admiration and ego boosting (Narcissistic Fuel) to keep their feelings of low self-worth from rising within themselves to the surface where they would have to experience these negative emotions. They spend all their waking moments seeking this positive praise (Fuel) to avoid dealing with their feelings of insignificance. Narcissists during the longest relationship phase of Sustained Devaluation use a variety of techniques to criticize confuse and demean their victim to control their victim, usually the Primary Intimate Partner. There is a lot to their manipulation techniques and different Narcissists use different techniques in different amounts to accomplish their goals, but there are many commonalities which Narcissists do almost as if they all attended the same Narcissism school. It is also important to understand the critical fact that 99.9% of Narcissists are unaware that they are in fact Narcissists because the defense mechanism of their affliction blocks out self reflection preventing them from accepting a diagnosis of Narcissism or even seeking a diagnosis (hey there is nothing wrong with me you are the one that needs help). The unaware Narcissists, or basically almost all of them, don't scheme and plan as much as people imagine, but are motivated instead by instinct and intuition. Their actions are driven by emotions which seem to originate from their subconscious reducing the ability of logical thinking to prevent or intervene in the Narcissists behaviors. In many ways they are on auto-pilot and they are unaware they even have a pilot.
There is much, much, much more to these toxic people and the suffering they create, but it is important to understand who they are so you can avoid them if at all possible, or limit their damage to you when not possible, because these people do leave chaos and destruction in their wake. Biggest take aways I can advise to anyone involved with a Narcissist is to understand they can not change because they don't have the physical brain area that would make it possible, they will create more suffering and hardship in your life than you could ever have imagined happening to you, and the only way to save yourself is to get away from the Narcissist by having absolutely NO CONTACT with them ever again. The tragedy though is that very few of their victims manage to escape to avoid this destruction because of the trauma bond they have formed with their Narcissists. It is scary stuff and difficult to comprehend it is so bizarre.
My advice to NobodysRage is to run from this relationship and don't look back. Let us know what you do and how it is going. If you stay I strongly suspect you are going to need good advice.