As the subject says? I’d like to use the default btrfs system, as is, to provide snapshots of the OS for recovery. But can I ALSO use timeshift in rsync mode to back up my home directory to a USB drive as well as leave the btrfs OS-only mode in play? Or is it only one or the other mode and that’s it?
You can do both, if you manually change the settings each time. 
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To be clear, so it’s either btrfs or rsync mode but not at the SAME time with different schedules?
That is correct, yes, or at least, if you use its own scheduling mechanism.
On the other hand, you could write your own scripts in which one script uses rsync and the other one uses btrfs snapshots, and then you can use systemd timers to run those scripts. But that’s going to be a complicated job, and to tell you the truth, even I, with over two decades of GNU/Linux experience, won’t go there.
Time shift is a system restore utility, use a backup utility for data.
https://wiki.archlinux.org/title/Synchronization_and_backup_programs
Yep, totally agree, and I have nearly 3 decades of linux experience. This would explain why mr google did not provide any satisfactory results. If I were to spend any time doing anything around redundancy and backups, I would investigate moving to ZFS instead (see my following post).
In fact, if I could get my iGPU to pass through to a VM I would just install Proxmox on my laptop and use a Manjaro/KDE VM as my daily driver. A local LAN based VM using Spice plays back a Youtube 1080p video reasonably well, with audio, so it’s pretty close to being usable even without GPU pass through.