How do I revert to Catalina from Monterey?

I have TWO questions re: issues migrating from Catalina to Monterey.

Some background:

I recently purchased a new MacBook pro silicon w/Monterey to replace my 2016 MacBook pro intel w/Catalina (originally w/Sierra).

In order to use Migration Assistant and copy my Time Machine info to the new MacBook, I was told I needed to upgrade the old MacBook running Catalina to Monterey, then back it up on TM. I did that.

I was able to migrate my files from my old TM/MacBook, and things seemed to have been working on the new, but today (2 days later) all my contacts and calendar items are missing on the new MacBook.

In the meantime, I've erased my old MacBook and re-installed a fresh Monterey OS for trade-in. :(

Now that the old MacBook has been erased/upgraded, it doesn't want to go backwards, and I'm having difficulty even restoring it to Sierra (it's original os) via internet recovery. If I Cmd+R, it only wants to install Monterey. If I Shift+Cmd+R, it appears to install Sierra, but it's never able to actually implement the older operating system, as it seems very confused and displays triangles and exclamation marks.

How can I restore my old MacBook? Can I use my old TM? I may have inadvertently deleted the Monterey backup folder. How can I tell what OS is backed up on it?

And... how do I copy my old time machine backups onto the new time machine? I tried connecting them both to my new computer and dragging and dropping, but it "prepared to copy files" for days and then just stopped. (Both are formatted Mac OS extended (journaled) w/ GUID partition.)

It's all a mess, and I'm at my wits end. Please help!