I then (just) get the options “Modify”, “Repair” and “Uninstall” - but, I do not want any of that, I just want to install (another) Python to a given directory.
It seems not to be possible to (easily) install two instances (in two different directories) of the very same Python version under Windows using an installer-exe – OK.
So, I thought, whether it is 3.8.10 or 3.8.9 might not be a too big deal and accordingly then tried to install 3.8.9 (which, in contrast to 3.8.10, is NOT installed on my computer yet) - see the outcome:
The german part says: “… - Another version of this product already is installed…”
Yeeeees, that’s true - and I do not want to remove said already installed version. Is it really not possible to install 3.8.9 AND 3.8.10 on the same Windows machine - simply using the two installers???
Correct, the installer is not designed to support that use case. It is designed for the vast majority of cases, where users want the latest version of a release series and for it to be updated when the installer for a newer patch release comes out.
The big question here is why you want to install multiple copies of the same version of Python. In most cases, it’s much simpler (and, in various ways, better) to make use of the venv module to create “virtual environments” that share the interpreter and standard library, but can install third-party packages independently of each other.
There are ways to get what you’re after here, but there will be compromises; most notably the lack of an installer. You may have better luck looking into the embeddable package distributed alongside the installers, but as I’ve not tried do do what you’re doing on Windows, I don’t have any specific advice.
I will note, though, that Python 3.8 is now in security-only support, and 3.8.10 is 4 releases behind already. You may be better served to build your own 3.8.14, or better yet upgrade to Python 3.10.