UUID=xxx does not exist. Dropping to a shell

When I tried to use a pendrive Ubuntu to figure out this problem, I finally found out that the hard drive wasn't recognized when Legacy Boot was disabled. This explained why manually choosing UEFI did work.

The problem was that the new motherboard had the default settings, so RAID was enabled. Switching to AHCI solved my problem. This were the steps needed to change it: (borrowed from This answer)

1. Boot into BIOS (F12 at startup)
2. Select Bios Setup
3. Move to System Configuration→SATA Operation and select AHCI

The answer is contained within your fstab file itself:

# / was on /dev/nvme0n1p3 during installation
UUID=dd84f4b3-d5bf-42e4-9b5e-ec685a461fad /               ext4    errors=remount-ro 0       1

# /boot/efi was on /dev/nvme0n1p1 during installation
UUID=B38D-559B  /boot/efi       vfat    umask=0077      0       1
# swap was on /dev/nvme0n1p4 during installation
UUID=f4134c38-10b9-478f-b550-54650a9f5140 none            swap    sw              0       0

so replace the UIDs with the oldfashioned names in your fstab:

# /etc/fstab: static file system information.
#
# Use 'blkid' to print the universally unique identifier for a
# device; this may be used with UUID= as a more robust way to name devices
# that works even if disks are added and removed. See fstab(5).
#
# <file system>  <mount point>   <type>  <options>       <dump>  <pass>
/dev/nvme0n1p3   /               ext4    errors=remount-ro 0       1
/dev/nvme0n1p1   /boot/efi       vfat    umask=0077      0       1
/dev/nvme0n1p4   none            swap    sw              0       0

and reboot.

If that doesn't solve your problem 100%, the true error lies deeper and you will have to compare your UEFI settings between the old and new MoBo.