You're exactly right. You need /boot/efi on nvme1n1p1. It is a 94M partition, just like the other drive. And the boot files are quite likely still in place.nvme1n1 259:0 0 931.5G 0 disk
├─nvme1n1p1 259:1 0 94M 0 part
├─nvme1n1p2 259:2 0 93.1G 0 part /mnt/6e6c4507-7bc0-4e22-95bb-2a6799bda688
├─nvme1n1p3 259:3 0 15M 0 part [SWAP]
└─nvme1n1p4 259:4 0 838.3G 0 part /mnt/81c74b42-8b66-40e9-9996-89982dbdb6cf
nvme0n1 259:5 0 931.5G 0 disk
├─nvme0n1p1 259:6 0 94M 0 part /boot/efi
├─nvme0n1p2 259:7 0 14M 0 part [SWAP]
├─nvme0n1p3 259:8 0 93.1G 0 part /
└─nvme0n1p4 259:9 0 838.3G 0 part /home
nvme0 is working, nvme1 does not. And I see why now. So, how can I get /boot/efi put back on nvme1n1p1?
I would probably physically remove nvme0... the working drive. Then see if the other boots on its own, or if you can select it from the BIOS Boot Menu. If you can't, you can boot on a live Linux Mint 21.2 flash drive and install grub back to your nvme1 and everything then should be back to normal. Or you might run Gparted from the live flash drive and use it to set nvme1n1p1 as your ESP... that may also make it boot normally again.
If you do remove the working drive, the remaining drive may be called nvme0 afterwards, and no longer nvme1. You need to check. This will probably make a difference if you install grub from a live usb.
@wizardfromoz can probably tell you how to run both Mint and Ubuntu together. He'll probably be along before too long now that I've rung his bell.
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