Thanks everyone for your great answers!
I've tried both ways (unassigned and root) to install Solus 4.3 (ISO dated Juli 2021) to the Mushkin stick, each time going into the installer with the stick pre-formatted to FAT32 and with msdos partition table. The Solus installer would, again in both cases (unassigned and root), overwrite the FAT32 filesystem with ext4 anyway. So after the installation neither Laptop nor Desktop would recognise it, despite having selected "install a bootloader" each time.
Again, while Linux recognises the stick and its contents fine with whatever filesystem is on it, both Laptop and Desktop BIOSes won't. Not even when I simply leave it empty with msdos partition table and formatted errorfree with FAT32. It simply won't show as a selectable option in the boot up menu (F11 or F12 during boot). At this point I'd like to think it does indeed have something to do with the motherboard firmware. The latest (available and installed) update for my desktop is from mid 2018, for the Laptop from 2012. But since I want to pass on the ready-made sticks, other people won't be able to use them either.
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Some tests I've performed trying to work through your answers:
After having furnished the stick with an msdos partition and a FAT32 partition table again (gparted), I tried using the console to set the block size for FAT32:
sudo mkfs.vfat -F32 -S1024 /dev/sdb1
mkfs.fat 4.1 (2017-01-24)
Warning: sector size was set to 4096 (minimal for this device)
Then, again preparing with gparted, I've tried it with ext4:
sudo mkfs -t ext4 -b 1024 /dev/sdb1
mke2fs 1.44.6 (5-Mar-2019)
mkfs.ext4: Invalid argument while setting blocksize; too small for device
Trying ext4 with 4096 bytes works fine as expected, smaller block sizes are not allowed, because the logical sectors are 'vendor set' and not changeable.
sudo mkfs -t ext4 -b 4096 /dev/sdb1
mke2fs 1.44.6 (5-Mar-2019)
Creating filesystem with 15591168 4k blocks and 3899392 inodes
[etc. more successful messages]
When trying to set block size while partitioning for FAT32:
sudo parted /dev/sdb --script -- mkpart primary fat32 1MiB 100%
parted warning:
The resulting partition is not properly aligned for best performance: 256s % 65535s != 0s
This would create an ext4 partition with an lba flag, not a FAT32 partition with the announced performance hit.
I'm assuming without my systems recognising the stick in the first place, Ventoy won't help either.
