I believe reinstalling it followed by using its uninstaller is definitely worth trying. It certainly won't make anything worse. I rather doubt it's going to help though, if the locations where it hides its stuff have been rendered off-limits in Catalina (or perhaps Mojave).
The other Discussion I referenced was never resolved, but it became too convoluted over its unproductive preoccupation with terminology.
- will the Time Machine backup have the same Avast software kernels still in it?
... probably... but it's not possible to know for certain. Any backup preceding its installation is likely to be too old to consider restoring. However, it is an essential prerequisite for advancing toward an eventual solution, which I suspect is going to be the scorched-Earth nuke and pave approach.
It might not be as bad as you might think, in that an erase and reinstall from scratch followed by migrating Time Machine's User Account information will omit the /Library/ files where you already identified Avast's recalcitrant components are hiding. That's identical to the approach I use for Macs that have been affected by any similarly categorized junk. It's usually the solution that results in the least amount of one's time and constant interaction.
The most important prerequisite is a Time Machine backup, which everyone ought to have anyway. Ideally, more than just one.
The fact you have at least some documents or work products in iCloud is also advantageous. That's the way Apple is going as far as a backup strategy is concerned. After all iPhones don't have Time Machine.