I bought a drive caddy so I could add a (smallish inherited) SSD into my laptop and keep my HD for storage of multimedia and such

My SSD has a fresh Linux mint install, my preferred OS. My HD has a Windows system on it + a big data partition.

Whatever I do, my laptop boots windows. Does not matter in which slot I put the SSD or the boot order. My laptop doesn't want to boot from the SSD (except of course when I take out the HD, then it has no choice)

Bleh. Back to GRUB again?

Are both Windows and Linux UEFI installs and SecureBoot enabled? Do both disks have an EFI partition? For this to work the way you want, you need a single EFI partition with a bootloader with both Windows and Linux entries.
It seems like your HDD EFI partition is seen first and has only a boot entry for Windows.
If you don't care about being able to boot windows, and you can confirm your SSD has an EFI partition (should be the case as you can boot with only the SSD installed), you could delete the FAT32 EFI partition on the HDD.

Also, I may have thought this was going to be on facial recognition login.

You could come over to the dark side and embrace WSL2.
https://docs.microsoft.com/en-us/win.../install-win10

Ah, no. The less windows I have on my computer, the happier I am. My idea was to boot into Linux directly and any exceptional time I needed windows, remove the drive caddy or change the boot disk order. That idea seems to not be working.

Both installations are efi. I don't have secure boot enabled, not sure what that does exactly or what difference it could make

If you have 2 drives with EFI partitions which only point to the OS on that drive, I believe only the first one the firmware finds on boot will be read and it will boot that OS (the behavior you're seeing). You probably need to remove the EFI partition from the hard drive and if you wish setup GRUB to have an option to load Windows in the boot config on your SSD. Deleting the EFI partition may kill your Windows install (or at least make it require a fair bit of work to make bootable again).

My suggestion: Copy HDD data to backup drive, remove SSD. Boot to USB bootable drive, wipe HDD, all partitions. Shutdown, reinstall SSD and boot. Install hypervisor of choice and create a Windows VM stored on the HDD to boot as needed. Copy data (not full partitions) back to HDD from backup drive.

Why secureboot matters: If secure boot is enabled and you have 2 OS configured for dual boot but only one of them has a signed bootloader, you'll only be able to boot the signed bootloader OS. Several Linux distros support secure boot at this point so its worth a look. Its not perfect but it can prevent some pre-OS methods of compromising a system.

My laptop really doesn't like Linux. A fresh install (wiping the disk before install) on the SSD just failed to boot and my system bricked, because there was no Windows backup OS. Maybe that was the reason I continuously booted into Windows. At the end I went back to install Windows first, then Linux with Grub2 and that works well. The HD in the caddy drive I emptied completely and now is one big NTFS volume for data

Another thing I earned is to hard switch off WIN10, because otherwise this NTFS disk is left in a state that Linux cannot mount it as a Read-Write volume

With secureboot enabled I was surprised to see I couldn't boot from the mint 20 install medium (written to a DVD).

ye I think windows just needs to be installed first

It is possible that your install disc is booting a BIOS installer instead of UEFI.
Try creating a USB bootable UEFI image for Mint Linux. If they don't have a signed bootloader you'll need to disable secureboot.
There should be no requirement for Windows to be installed. You just need a properly configured UEFI bootloader with an entry for your Linux install.
https://www.itsmarttricks.com/how-to...%20to%20Fat32.