Doing some testing here. I have LinuxMint 21 Cinnamon on /dev/nvme0n1 with p1 being the EFI system partition and p2 being the BTRFS system partition.
I installed EOS-Cinnamon on the same system but I picked the second drive /dev/sda. During the installation I created an EFI system partition as /dev/sda1 and the btrfs system on /dev/sda2.
Some how the EOS installation changed the BIOS default boot drive from /dev/nvme0n1 to /dev/sda. So EOS boots by default and I have to use F11 to popup the boot menu to select the /dev/nvme0n1 drive to get LM21 to boot.
I’ve tested changing the default boot drive in the BIOS and that works, but am I correct in that the EOS installation does indeed change the BIOS boot default setting during installation.
The info you gave (EFI partition) suggests you have a UEFI system, but you are referring to it as BIOS and assume it works like BIOS (boot drive).
If you are on UEFI, there is actually no “boot drive”, but “OS boot order”, no matter on which drive they are on.
As @pebcak said, the last installed OS sets itself as 1st in “OS boot order”.
You can change “OS boot order” from inside Linux, using the efibootmgr command line utility.
Info: man efibootmgr
Some UEFI vendors make them work like BIOS, only providing a boot drive to select, but this is just a bad implementation. The UEFI (Standard) can and should work as we have described.