I don't think her work sounds bizarre.
If its a large organization with 100s of employees, many of whom are hybrid workers without a fixed schedule of in-office days, and there's a minimum requirement of in-office days per month, then you need some sort of system.
Even if it there was no minimum in-office requirement, Employers need to know who is on-site, on any given day. With a large organization, security passes are a lot more efficient for everyone instead of employees having to manually let their employer know if they're coming in, and have someone manually prepare a daily log.
It may vary by business type, but I also don't think that it's "bizarre" for an Employer to have a minimum requirement of in-office days per month and, if they have that requirement, monitor it in someway. Again, security pass log are likely the easiest and least intrusive way to do that.
It looks like the policy, that security pass logs would be used for monitoring, was negotiated with the union.
The OP's immediate manager was, initially, implementing the policy to the letter (which I think is understandable for a low-level manager, whose job is to implement policy, and even more so with a policy that the union had a hand in forming).
It was the OP who, without being asked, voluntarily sent them a screenshot of transaction as "proof".
From there, it seems like the jnr manager was not sure if they could accept it (or at least, wasnt confident in doing so without approval from his manager), so sent the screenshot to his manager, to see if they could accept it despite the policy.
Middle manager, seemingly, says "This could work, but the screenshot only shows that someone made an on-site purchase. Ask OP to send a bank statement, so there's a record it's in her own name".
Up to that point, I don't see any issue whatsoever, and I also think its a very reasonable request in the circumstances. OP can redact everything else, she's just being asked to give her Employer two peices of information she has already given them.
I'm not entirely clear what has happened since then - it isn't obvious to me that they've been demanding anything or just explaining that if the OP doesn't want to (or cant) prove she was there, she needs to make up the day.
I agree that the OP has acted bizarrely, though. If she hadn't already given them the transaction details it would make more sense.
Probably a good thing she's in a union because her manager and manager's manager probably now think she's most likely dishonest and, if not dishonest, extremely irrational and awkward. Still, a good time to job hunt....