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