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I would think you could put /usr on a separate disk just fine, as long as it was available to mount at boot time.
How small is your SSD that you're trying weird stuff to save space? Even in the tens of gigs should be enough to run Ubuntu. I just checked two full desktop systems, and they are 32 and 24 GB used for the root partition.
You didn't mention why you're trying to bind-mount your /data volume from your initramfs environment, but the only reason I can even guess at is that you're trying to use it as part of your recovery environment. In which case, you'd probably be better served by doing the recovery from an Ubuntu live usb rather than try to cobble together a working environment from the shrapnel you left scattered across your drive.
This process should literally look like -- boot, mount drives, rsync /usr back to root volume, clean up fstab/any other config changes, reboot, try again later after you've done more reading.
I'm surprised you can't put /usr on a separate partition. Back in my SunOS days, we used to NFS mount /usr on all our workstations.
There was a movement to make /bin /sbin etc symlinks to /usr a few back. I honestly don't remember the rationale, but here's Debian's page about the change: https://wiki.debian.org/UsrMerge. If I hadn't been following the distros at the exact moment they did the changeover it probably would have thrown me for a loop too.
I think it had to do with the fact that these days relatively few people need /usr on a separate partiton and so it very rarely happens and something about system binaries being easier to manage if they're actually all in one place. People are ready for some tweaks to the FHS, I guess.
Have you considered btrfs compression?
I’m not too familiar with Ubuntu, but the arch wiki has a section about moving /usr to a separate partition: https://wiki.archlinux.org/title/Mkinitcpio#/usr_as_a_separate_partition
Maybe using these instructions, you can still offload /usr to a mechanical drive.
Just out of curiosity, how large is your /usr directory? Mine is only 30GiB (arch Linux, kde plasma with all apps + hyprland), which only takes up 17GiB on my disk due to btrfs compression (zstd level 15).