There's a book that I encourage everyone to read called Motivational Interviewing. I've read the 3rd edition and I'm currently working my way through the 4th edition to see what's changed, because it's a textbook that they basically rewrite completely with each new edition.
Motivational Interviewing is an evidence-based clinical technique for helping people move through ambivalence during the contemplation, preparation, and action stages of change under the Transtheoretical Model.
In Chapter 2 of the 3rd Edition, they define Acceptance as one of the ingredients for change, part of the "affect" of Motivational Interviewing. Ironically, people do not tend to change when they perceive themselves as unacceptable as they are. It is when they feel accepted as they are that they are able to look at themselves without feeling defensive and see ways in which they can change and grow.
Nearly all that they describe in chapter 2 is affective—it is neither sufficient nor even necessary in the clinical context that the clinician feel a deep acceptance for the client within themselves, but the client should feel deeply accepted so that they are given an environment in which they can grow. The four components of the affect of acceptance are autonomy support, absolute worth (what Carl Rogers termed "Unconditional Positive Regard"), accurate empathy, and affirmation of strengths and efforts.
Chapters 5 and 6 of the third edition define the skills of providing the affect of acceptance defined in Chapter 2—again, not as a feeling, but as a skill. It is something that can be taught, practiced, and learned. It is a common misconception to believe that unusually accepting people become therapists, but what is actually the case is that practicing the skill of accurate empathy trains the practitioner to be unusually accepting.
The chief skill of accurate empathy is that of "reflective listening", which essentially consists of interpreting what the other person has said and saying your interpretation back to them as a statement. For an unskilled listener, this might be a literal rewording of what was said, but more skilled listeners can, when appropriate, offer reflections that read between the lines. Very skilled listeners (as measured by scales like the Therapist Empathy Scale) will occasionally offer reflections that the person being listened to did not think, but will recognize within themselves once they have heard it.
In that sense, in the way that we measure empathy in settings where it is clinically relevant, I've found that AIs are very capable with some prompting of displaying the affect of accurate empathy.