Is there a source for this?
Transgender Kansans had their IDs invalidated overnight, causing confusion and panic

Some transgender Kansans received letters urging them to request new IDs that conflict with their gender identity and presentation, because their current ones are "invalid immediately." It’s the result of a new law that also regulates which bathrooms transgender people are allowed to use.

Kansas Public Radio

I’m still baffled by the fact that for most US citizens, a drivers license is the only government ID they have. It’s not that hard to issue an ID card to everyone and when everyone is required by law to have one, it’s way harder for rogue lawmakers to take it away.

Here in Germany we’ve had mandatory ID for decades and it works really well. Even if our government suddenly decided that being trans isn’t acceptable anymore, the worst that would happen in that regard is that your ID card shows your deadname (gender isn’t listed explicitly). Sure, that sucks (a lot!) but at least it doesn’t take away people’s ability to vote or otherwise identify themselves.

The Kansas thing also invalidates state-issued IDs, not just drivers licenses. Usually it’s redundant for people to get both, and that wouldn’t have helped in this situation anyways.

One could also present a passport or military ID, but the former was also being invalidated for trans individuals by Trump, and the latter applies to almost no one, given the difficulty of simply existing as a trans person in the military.

Okay, that changes my first sentence a bit but the rest still stands. Because as a German I am required by law to have valid ID and the government is required to issue one to me, it would incredibly hard to invalidate any ID that they themselves issued without providing a replacement.
You see, in the US, we’re required to have ID as well, but we have to pay for them, keep them updated, etc.
It’s the same in Germany, it costs about 40€, you have to fill out a formulae, you have to go to the citizens office, you need to get it updated if you move places and you need a new one every 10 years or so. The only difference is, you require it in your daily life - when there is a control of your bus ticket, when you want to buy alcohol, went you get a room in the hotel etc. Life would be pretty complicated without an ID, but I think there are also people who give a shit. So it’s not like everybody has an ID (most do) and also it’s not like the state sends them for free to you via mail.
Yes, this is the exact same in the United States. There is no difference. Except may that if you are pulled over by a police officer without ID, you can be fined or even arrested. Otherwise, what you have described is the exact same situation as the U.S.