Windows 10: Can I move an EFI partition that's on the wrong drive?

Hello,

Recently I built my new computer with an M.2 SSD (for Windows), a SATA SSD (for games) and a normal normal hard drive for general files.

After installing Windows 10 20H2 I noticed that the M.2 SSD (with the boot and recovery partition) disappeared from the "boot selector" in my BIOS (Gigabyte B460M Gaming HD) along with the HDD, just the games SSD is appearing in the "boot selector", but Windows is booting fine from the M.2 SSD. I only noticed that the two other drives disappeared from the BIOS boot selector after I did a BIOS update, but I believe this problem with those drives disappearing started after I installed Windows and not because of some BIOS problem since the BIOS still detects all three drives, but only gives option to boot from the games SSD.

When I was installing Windows 10 on the M.2 SSD, I ended up deleting some partitions (on Windows 10 installer menu) from the games SSD and M.2 SSD to allocate more space for them. All three drives (M.2 SSD, games SSD and HDD) were connected at that time and I think Windows might have mixed things up with the EFI partition. I also noticed on Windows Disk Management that the EFI partition is on the wrong drive. The EFI partition in on the games SSD, while the boot and recovery partitions are on the M.2 SSD that is the one with Windows installed. The HDD only has one primary partition, no other partitions.

I believe the reason why I can only see the games SSD on the boot selector from the BIOS is actually because it's the only drive with an EFI partition now and from what I understand (correct me if I'm wrong), but if I disconnect/remove the games SSD from my system, Windows won't boot at all, even with the boot/recovery partition in the correct drive (M.2 SSD).

TLDR:
- Installed Windows 10 on the M.2 SSD while having other two drives connected at the time (SATA SSD and SATA HDD).
- M.2 SSD has the boot and recovery partition (and Windows), while the SATA SSD has the EFI partition and another partition where I store my games.
- Boot selector from the BIOS only shows the SATA SSD (with the EFI partition/games) as a bootable option, but still recognizes all three devices as being connected.

So far I'm not having any boot problems even though the M.2 SSD is not appearing on the boot selector, but appears on everything else and I actually don't know if "if it ain't broken, don't fix it" would be the better option right now, or if I should move the EFI partition from the games SSD to the Windows M.2 SSD, if possible, to "make everything to be in order".

I also wanted to ask if this could possibly solve my problem of not having the M.2 SSD showing up in the boot selector.

:)