Which, at least in American English, comes across like corporate jargon/weasel words. Lost their job is literally true and would probably take a bunch more words to describe the precise reasons.

Both things can be literally true. I've lost my job by being made redundant, twice. In Britain redundancy is a very specific thing, where your role no longer exists and you must be let go in a fair way according to employment law. It's quite the opposite of jargon or weasel words here: https://www.gov.uk/redundancy-your-rights

Synergized is the term I typically hear.