It's also correctly seen by Windows.

It's set to auto-detect in the BIOS Setup, but whereas the other drives are correctly specified in the BIOS Setup, this drive says "None".

The HDD is jumpered as Master on the Primary IDE controller.
The CD-RW is jumpered as Master on the Secondary IDE Controller and on the end connector.
The CD-ROM drive is jumpered as slave on the Secondary IDE Controller and on the middle connector.

It's not a problem because everything APPEARS to be working fine, but I don't like things that are behaving oddly, I'd rather find out if something is broken and fix it.

No worries. The BIOS should not be set to 'autodetect' for optical drives as it can only autodetect hard drives. If it bothers you, go into the BIOS setup, highlight each entry for the optical drives and change to either CD-ROM for a drive which reads only CDs, or to DVD-ROM for a drive which reads both CD and DVD. Note that even if one of the drives is a burner, the BIOS will probably not have this option in the drive settings. It only gives you either 'CD-ROM' or 'DVD-ROM'. This is quite normal. It won't do any harm to leave the BIOS as it is now, but by entering the correct drive types (instead of autodetect which it can't do) the PC should boot up a little faster as it won't be struggling to identify the optical drives.

"The BIOS should not be set to 'autodetect' for optical drives as it can only autodetect hard drives."
'fraid not, it detects the CD-RW just fine, and correctly shows the details of the drive.
My other [even older PC = 1997] shows the auto-detection on-screen during startup. Lists 2 HDD's with descriptions, 1 CD-RW and 1 CD-reader correctly identified and described.
This newer Hewlett Packard [1999] doesn't display the detection on-screen during startup, it only displays the details within the BIOS Setup.
Before I fitted the CD-RW, the CD-reader details were previously displayed in the BIOS Setup [when it was jumpered as Master] as follows:

"Secondary Master = [CD-ROM 52X/AKH - (SM)]"
[I wrote down all the BIOS Setup settings back then.]