With all you tried I am no longer ruling out a hardware problem.
You tried already an different Linux distribution, do you have the option to run Windows? If not, you could try something like NomandBSD.
The other option is to use USB Sound Card, I am using one with a build in amplifier in a quest to have a “more minimal setup” that is still good enough.
Bonjour deano_ferrari and marel! 
Thank you once again for being here to help me. 
This is the “input devices” tab of Pavucontrol-Qt on Olive, my new computer:
The first input, marked “connected”, corresponds, I presume, to my portable monitor connected via USB-C DisplayPort. It’s not equipped with a microphone, as far as I know, only an audio output jack port:
The second input, marked “connected”, corresponds, I presume, to my Audio-Technica ATH-GL3 wired headset plugged in via Olive’s front Jack port. There’s also a “line out” marked “disconnected”, which I don’t know anything about:
The third input mentions a “front microphone” and a “rear microphone”, both marked “disconnected”. This input is the only one left when I filter out “hardware input devices”:
It is also the only one to show activity via its bar for the “front microphone”, which moves slightly:
And the one for the “rear microphone”, which moves even more:
Unfortunately, these two activity bars don’t react when I speak into the microphone of my headset.
As the link shared by deano_ferrari suggests, I tried muting one of the two channels of each input and then rebooting to test whether a microphone is correctly detected by the Discord software. First the left one:
Then the right one:
Unfortunately, these settings are reset on reboot, with the exception of the “rear microphone” setting, which is retained, and no working microphone is detected by Discord.
Perhaps there is a more appropriate way to disable these audio channels?
Marel: I have Windows 11 installed on a small partition on Olive, my new computer. I use it to install EFI updates. My microphone is detected here and working.
I also booted ISO images of Fedora 41 and Kubuntu 24.10 on Olive to test microphone detection. The bug is present as on openSUSE Tumbleweed.
Marel: I forgot to tell you about the USB sound card. Thank you for the suggestion. I’ll buy one if I can’t find a solution to my problem. 
I asked for help on Pipewire’s Matrix room. It was explained to me that the two inputs named “monitor” in Pavucontrol-Qt on my computer are loopbacks.
I was also invited to install hdajackretask, but I don’t know what to do with it yet:
