I like UUIDv7s as database IDs since they sort chronologically, are unique, and are efficient to generate. My system chooses the UUIDs; I don't allow externally generated IDs in. If I did, then an attacker could easily force a collision. As such, I only care about how fast I create IDs. This is a common pattern.
If your system does need to worry about UUIDv7s generated by the rest of the universe, you likely also need to worry about maliciously created IDs, software bugs, clocks that reset to unix epoch, etc. I worry about those more than a bonefide collision.
Your app is must be popular to be having an entire universe "amount" of users lol
joke aside all of this is theorical, in practical application its literally impossible to hit it that it doesn't matters if its possible or not since you are not google scale anyway
Only if the other side uses your key as theirs, and uses it to store data from many sources. I, personally, don't feel it's hardly worth considering. A primary key under your own control doesn't cost much, and is a better choice.
The entire universe. Else it's not universally unique.