Just turn off formatting of the mentioned partitions and add a Root one?
That's pretty much it, yeah. Though there are some caveats:
Be sure neither distro leaves the swap partition in a mess for the other to find. Not sure of defaults, but the swap partition can be configured as the storage location for hibernation data. Though worst case is probably just ...
I managed to fix the issue with the help of the comments. Thank you all! For completeness, I quickly state all the steps I took to fix this:
Quickfix - If you quickly need to boot without solving the actual problem
Insert a livestick with a functioning bootloader (I used Ubuntu 20.04 with GRUB)
Once the GRUB from the livestick started, interrupt the ...
Speculation: Using multiple EFI Partitions is a non-standard approach and can lead to some issues. AFAIK, GRUB should still be able to work with that - however I couldn't find the issue here and I don't have a working setup for reference.
Alternative solution without GRUB
rEFInd is a boot manager that I can confirm to be able to handle multiple EFI ...