Is a copy of /Library and ~/. sufficient for a clean install?

The title says it all. After too many OS X and now macOS upgrades-in-place, my disk is cluttered with too much history. There is also the occasional small but unnerving issue that may just be resolvable by a clean install.

Moving from Catalina (10.15) to (10.16 version 11), my plan is to save just /Library and ~/.. Is any other path necessary to maintain personalized settings?

(After upgrading disk-to-disk—as opposed to time-machine-to-disk—I haven't been able to continue using my Time Capsule histories, and hence I'll be wiping these and starting fresh.)

Yes, a copy of /Library and ~/. (which includes ~/Library) will retain most of your personalised settings. You may want to also include /Users/Shared as it is used by a few apps (e.g. from Adobe) to store licences and/or settings.

But the copy will include much of your clutter and history. This will defeat the purpose of a 'clean' install.

A clean install requires you to erase the disk, reinstall macOS, reinstall applications and recover your documents, photos, etc. (but, sadly, not settings) from your backup. This process will require you to enter application licenses and re-establish settings.

You need to judge whether the time and effort of a true clean install is worth it for you.

Personally, I do a clean install every 18 months or so - but that is because I am something of an app junkie.

Some of /Library may not be copyable (or replaceable) due to SIP. And if you do copy back files, you might inadvertently overwrite files that needed to change in the update.

A better approach would be a TM backup → erase → install → use migration assistant to restore account and settings from backup.