Assuming their story is true.

How would logging in and giving them your number potentially restore them if they're stored locally and are just gone?

Do you even understand the meaning of secrecy? And the point is that you cannot enter the Signal without authorization by phone... And in general, no one cares about your messages (what is inside), the main thing is who, with whom and when. You will be imprisoned not for what you wrote to Osamma en Laden, but for the fact that you contacted him at all (then turn on your imagination and find some other international villain)

I'm using the same device, I stopped using signal about a year ago, my phone has updated versions a couple times since then, every couple months I would go back to find a password or login that I was texted, a couple days ago I started signal to look for a login and it said it had to update, now it says I have to "secure your number" and use it to log in to retrieve my messages.