I may end up going in deep anyways and replacing the 500GB HDD with 1TB HDD that I have on hand. Then, that would be a good Time Machine piece.
How much data do you have and will be using in the foreseeable future? If say only 125 GB, then I wouldn't bother swapping out the 500 GB hard drive. They say you really only need about 2-3X the capacity of your data used. 500 GB / 3 = 167 GB. However, if you plan on having say 500 GB on your boot drive, then yeah, a 1 TB Time Machine drive makes sense.
Please post your results once you have Monterey installed on the SSD. I'm curious how well it does on 4 GB RAM.
I note that even way back with Sierra/High Sierra my older machines with 4 GB RAM would encounter the beachball from time to time even with SSD and just relatively light usage, meaning a few browser tabs, mail, MS Office, Calendar, Mail, and Calculator open. These beachballs disappeared with 8 GB RAM with this type of usage.
This is what I'm using right now with 8 GB in Monterey with usage similar to the above, also with Photos, Citrix, and Music open, but without MS Office (since I don't have an Office license for this machine):
It's got some compressed RAM, but no significant swap, and is only using 6 GB physical RAM total with green memory pressure. Overall the machine feels very responsive, and there are no beachballs.