Both the State Department and the UK High Court agreed she did.
The US and UK even changed the rule to remove diplomatic immunity from spouses of people at that base after the incident (but not retroactively), which proves she did have it at the time.
I’m not aware of High Court determining that. I’m aware of American court proving that she didn’t. The State Department doesn’t have any reason not to lie, given that they facilitated her escape.
https://www.craigmurray.org.uk/archives/2019/10/the-foreign-...
(And say what you like about Craig Murray, he was an ex-diplomat so should understand the rules around immunity).