How does a sender who only has a GPLv2 license notice even know that there is a v3? Should they first send a letter asking which versions are available?

the usual license header has something along the lines of "either version [23], or at your discretion, any subsequent version", which clearly explains that there are specific versions with distinct rules. Many people opt not to include this clause because they (understandably) don't want to automatically agree to a contract that hasn't even been written yet. However if they fail to make the version clear that's on them.

Anyways I don't think this defense would ever fly in court. As soon as the plaintiff's lawyers produce evidence that you are aware of GPLv3 (such as pointing out that you have GPLv3 software on your PC or phone) the judge is going to see that you're trying to game the system on technicality and sanction you. Judges really don't like this sly loophole BS where it's extremely obvious that you're feigning ignorance for the sake of constructing an alternate reality where you hypothetically never knew there was a GPLv3.

If the sender requests GPLv2, he should receive GPL version 2.

If the sender requests GPL, I find it natural for him to receive version 3, because it's the latest version. At the time of receiving the license, he gains knowledge about the existence of version 3 (the header on the print says the GPL he received is version 3).

If the sender has a notice about GPLv2, it means that there's a high chance that there's also GPLv1. This should be a sufficient hint that requesting only "GPL" is not sufficient, because the sender should be aware of the risk of receiving GPLv1 if he won't mention the "v2".