You can usually (in newer modules) derive it from the inscription of the module shield, though.
I figured as much from here
https://docs.espressif.com/projects/esp-chip-errata/en/latest/esp32/01-chip-identification/index.html

But does that mean I can't reliably determine how much PSRAM my module ...

How do I reliably obtain the Ordering Code or Manufacturer Part Number for my particular module? The closest way I've found so far is by running esptool chip-id, but it seems to be missing information about the PSRAM of my vanilla ESP32.

Tying it down to e.g. the ESP-IDF repo means (or at least implies) that the discussion is intended to be only about ESP-IDF.
Possibly. One could argue that you could even open discussion-only repos if that's a significant issue, but even with the downsides of it being IDF-centric, the unification ...

This is a complete redundant stubborn waste of resources by Espressif, and I already went over why and how this could be better addressed here
https://esp32.com/viewtopic.php?f=2&t=41496

Everything that goes in the here is a candidate for a Discussion on one of the Espressif repos, in addition to every issue that is filed in IDF repo that should go here, which is the first reason for this. And let's face it, Espressif's GitHub, especially ESP-IDF repo, is more popular than this ...

Interesting. Just had the same problem, no virtual machine or anything, though, and switching to a USB3 port did it for me. Still looks like a bug, though.

There should be an easy way to find out, right?
I wonder how quickly you gave up on looking for that, if at all.
There are at least 3 ways I can think of:

$ xtensa-esp32-elf-g++ --version
$ idf_tools.py list
Check the folder name under <folder where idf tools are installed; defaults to ...

So will this ever happen?