Before joining

No you don't.

I can go to the corner shop/local garage right now, buy a SIM card for 99p and then buy a top-up voucher in cash to have a completely anonymous phone number.

Albeit is the UK in Europe again? 🙈

edit: where I would be worried if my privacy was on the line is I could also go to the local pawn shop / Cash Converters to ensure that SIM card isn't associated with an IMEI I've previously used and buy in cash a cheapo phone.

So what? The law enforcement knows you have an account and knows the sign up date and last login. That doesn’t affect your privacy whatsoever. Besides, Europe isn’t a monolith. You can absolutely buy and use a SIM card without disclosing your name in some countries.

But, again, all they can prove is that you signed up to Signal and when you last signed in.

Exactly. Signal is private, not anonymous

I believe the same is true in the US.

Sometimes, but that's it. Authorities and signal itself can only say "this number has account with us since $signupDate and used it last on $usageDate". Signal can't say "we know $number is talking to $otherNumber" nor can they say "$number is in $group talking to $users".