There is some question as to whether Anne Sacoolas had diplomatic immunity at the time of the incident. However, the UK's foreign office has said that she did, and theirs is effectively the last word on the matter. Courts do not typically question foreign ministries on matters of international relations.
However, diplomatic immunity is only perpetual for official acts. Her immunity ended when she left the UK, which is why the prosecution could proceed.
US civil claim
In general, the existence of a criminal trial doesn't cause a civil claim to be dropped. This case is not still in progress, however, because the parties reached a settlement. See for example Harry Dunn family reach deal in US civil claim against Anne Sacoolas from the Guardian.
The US has ruled out extradition in this case. From the previously linked article:
In December 2019 she was charged with causing the 19-year-old’s death by dangerous driving, but she refused to return to the UK to face trial and the US government refused to grant an extradition request in January last year. This year Biden’s administration maintained that the decision was final.
Trial "in absentia" (actually by video link)
This is covered ably in James K's answer.
Enforced participation and sentencing
In fact, it seems that there is no enforcement, but rather voluntary submission on the part of Anne Sacoolas, as shown in the rest of this answer.
- While Trump was clear he would not allow extradition, it sounds like the political or justice dept mood has changed, or something's been agreed settled, so there is now some kind of UK-US consensus that law enforcement jurisdiction, legal action and enforcement of process, is possible in one or both countries. But what changed?
Possibly the abovementioned settlement, whose terms have not to my knowledge been disclosed. Among the terms of that settlement may have been an agreement on the part of Anne Sacoolas to submit to the jurisdiction of the British court in the criminal prosecution. Regardless, the option was always on the table for her to submit voluntarily to the court's jurisdiction, and perhaps she is truly doing it of her own free will. Or perhaps she is doing it on the secret instructions of the US government -- she is after all reported to be a (former) CIA agent -- in order to put the diplomatic conflict to rest.
- Is it now a settled matter that AS is voluntarily or by operation of law, to face the UK criminal justice system in trial? Again, what happened politically/legally to lead to that?
Well she has pleaded guilty, so yes, her submission to the UK criminal justice system is settled; the verdict has been reached, and all that remains is for a sentence to be imposed. From the New York Post's article US diplomat’s wife Anne Sacoolas pleads guilty to death of Harry Dunn:
She was told by the judge that she had shown remorse by an early plea of guilt and by taking part in the court process, which she could not be compelled to do.
What happened legally is that she consented to be tried remotely. What happened politically is a matter of conjecture.
- It seems odd that someone would be at trial if they weren't exposed to a courts sentencing power. And, if so exposed, it seems odd the court would choose a virtual attendance for a defendant not an in-person one. That more than anything confuses me. Why virtual, in this case? What does it signify?
At this point I believe she has three options: (1) attend the sentencing in the UK (assuming she's given leave to enter) and risk being imprisoned, (2) remain in the US -- that is, not submit herself fully to the court's sentencing power -- and risk a harsher sentence, which then increases the likelihood of being sentenced to serve prison time, leading to (2a) return to the UK to serve her sentence, or (2b) avoid going to the UK.
Since she voluntarily submitted to the trial, it probably makes more sense to voluntarily submit to the court's jurisdiction by attending the sentencing.
Some articles have said that the judge ordered her to appear in person for the sentencing, but a more detailed account suggests that this isn't true. Rather, according to this account, the judge has strongly implied that appearing in person will lead to a lighter sentence because it is a more sincere showing of remorse. From the Guardian article Anne Sacoolas pleads guilty to causing death of Harry Dunn:
Mrs Justice Bobbie Cheema-Grubb told Sacoolas at the end of a brief hearing at the Old Bailey that there was nothing to stop her from attending a sentencing hearing during the week commencing on 28 November.
“The personal attendance and voluntary surrender to the court of Mrs Sacoolas would provide weighty evidence indeed of genuine remorse,” said the judge, who added that the offence carries a maximum sentence of five years’ imprisonment, although she noted the range of sentencing guidelines is from a medium-sized community order to three years’ custody.
I say "assuming she's given leave to enter" above because, despite the judge having said that there's nothing to stop her from attending her sentencing hearing, there might in fact be something. The immigration rules (9.4.1(c)) require refusal of leave to enter if the applicant:
has committed a criminal offence, or offences, which caused serious harm.
I would assume that there should be some exception that would apply in this case, but I couldn't find it. Since it's probably, uh, rare for criminal defendants to enter the UK voluntarily to attend their own trials, it may have been overlooked. And while I found a provision that allows the Home Secretary to make individual orders to refuse leave to enter, I did not see a corresponding provision to allow individual orders to grant leave to enter. If I were Anne Sacoolas or her lawyer, I would seek to clarify this before planning to go to the sentencing hearing.