MacOS Sonoma (Studio) does not show external drives that are mounted

I have a recurring bug with external drives. They sometimes do not show up in finder - that while they are mounted and can be used by programs like Photoshop and CCC. An example.

To recap: Finder is not correct, a back-up task uses the drive anyway. And Lightroom sees it too.

It is part of a wider problem, that I have with other drives too, that either do not mount, are not seen, but when I detach the USB-C cable, the computer cries out loud.

Or drives that upon waking of the computer, are reported as missing such as mt WD-Blue sata time machine disk). While the Apple Support was not able to help me: good luck with your Orico/Hagebis etc drives. .

System: Studio 2022; Sonoma.

My question is: how can I tackle these problems, that I have so sparsely stated, I'm sorry, this is a longer problem, too many failure modes already for me to recap; and this keeps me from updating my computer to Sequoia; and IN FEW YEARS, replacing it . .

OK I'll try.

1. As regards the TM SSD, I had a SATA 2.5" in a Orico/Hagebis mini-format house. It stated to give problems in not being mounted. The disk and house are OK, I now use that drive on my wife's iMac. Maybe:: It is just that the Studio sends out commands that get a time-out, and processes are not finished, or something like that. Anyway, after sleeping the TM will not show up and is not there for the backup. Failure.
2. After finding it on my M3/Sequioa machine, I cannot run DU repair, nor reformat, nor add volume/partition, not on volume nor on disk nor anything.
3. On the old iMac ai can directly see it, I can change the name, but no - I cannot reformat the TM disk.

A WD Blue 2Tb disk of € 200 gone in thin air??

I hope you will not ask the error codes.