I think the performance under Catalina versus Monterey will likely be equally bad with an HDD. It might not be slower than what you have right now, but it might be. This is because both Catalina and Monterey will insist on configuring your internal drive to APFS, which is very slow with HDDs. If your internal drive is already APFS (try get info on the HDD) then what you get now may be similar to what you will get with Catalina or Monterey.
You have three options since it sounds like you will be advancing one way or another to Catalina or Monterey:
(1) Keep using your internal HDD. If the performance for what you use it for is acceptable, that should be ok.
(2) See this post by Jack19, Use an external SSD as your startup disk … - Apple Community This is a well known and imminently acceptable solution which entails purchasing an external SSD and using it as a boot drive. This will likely improve your Mac's performance by a factor of 5x-10x.
(3) You can also do what I did with my 2015 iMac, which is take it to a neighborhood Apple Authorized Service Center (these are Apple-certified shops, they are usually willing to work on older Macs, Apple will not do this kind of work on a Mac as old as yours) and they installed a new internal SSD to my iMac. They also returned it to me with Monterey installed so I simply migrated from a Time Machine backup and was back in business immediately. The cost for this was about $75 (I had already purchased the internal SSD myself, 1 TB for about $100). The total for this came out to about the same as getting an external SSD would have cost. I recommend having an Apple-certified technician do this on an iMac because of their special tools and experience, but ordinary users have done this type of work themselves if they are savvy about it and have some experience.