"Plug'n'Play" webcam working fine on Lenovo Box with Mint and Windows; the second box, a Dell, with Windows, MX and Manjaro, they all need to reboot to detect it. Even Windows.

What kind of hardware issue might I be looking for here?

It might help to know the specific model of that computer.

System info:
Machine Dell Inspiron 5676
Operating System Manjaro Linux
Cinnamon Version 4.8.4
Linux Kernel 5.9.16-1-MANJARO
Processor AMD Ryzen 7 2700 Eight-Core Processor x 8
Memory 15.6 GiB
Graphics Card Radeon RX 580X

Probably should post the make and model of your webcam as well. Since you have the same result in both windows and linux, it's not an OS specific issue. Have you tried using different usb ports and see if you can get the webcam detected?

One other thing to try is connecting to a USB2 port instead of a USB3 port. I know USB3 is supposed to be backward compatible but I've encountered some problems with devices originally designed for USB2 functioning improperly when connected to a USB3 port.

The other thing to look at is the usb settings in your bios setup, perhaps legacy bios settings. Check your manual for usb related bios settings. It's very odd that on reboot with the webcam connected the bios apparently detects the webcam and both windows and linux can see the device but not otherwise. Almost sounds like some type of security thing for webcams or usb devices. You can always call Dell support since the issue arises on windows. They may be aware of some setting in the bios that would cause that behavior.

You definitely should post webcam make, & model; also whether ut's usb 1, 2, or 3.

Most webcams respond to the uvcvideo.ko module, so no harm to run Also, whether internal or external, nearly all should be on some part of the usb bus, so the output of lsusb is needed, after adding the uvcvideo module.

once again, I had to do a win95-style full re-install to get this working
it seems Manjaro only installs properly sometimes on this box.
no idea why, can't find any hardware issues but this machine definitely has them.
all working once again. box is being phased back to Windows and replaced.

So you're selling it off? Mark this solved then. Linux purists may not love it, but it's a solution.

Some distros seem to actively discourage users from getting to grips with problems. If your problem isn't solved by point & click, you find yourself up against some massive & intricate subsystem like systemd, which reaches into everything and may have been tweaked by the distro for their system.

Consider your choice of distro in that case. Slackware (which I use), Arch & others use vanilla packages. Slackware uses systemV init, easier to poke at imho. You need support initially, but you can get it.

No, not selling it. Have students in the house and the schools are Windows-centric. It runs AutoCad really well.
Oh, boy, do I here you on this.
And some Linux help sites are plagued with people who like to show off their leetness (not naming any )