Depends on what's your goal. Privacy and the least amount of paperwork? Probably a place like Wyoming, where your annual report is a single page saying "yeah I'm still alive". But an LLC will usually need to be parallel-registered in the state it's doing business in, so if it's a pain-in-the-butt state like California, might as well register it here - you're not escaping their fees and paperwork either way.
Delaware is for big companies.
If you live in California, you likely have to register in California. So you really only have one option, unless you want to register in two places. You’ll also have to pay at least $800/year for the pleasure.
The follow-up question then is... what are the legal workarounds to avoid having to also register it in one's home state, e.g. California? Surely there are some.
This is kind of California specific. There isn’t really a work around if you’re “doing business” in California.
Does this imply that any business that's not registered in California can't do business in California?
Um, it implies that if you’re “doing business” in California, you are required to register there? “Doing business” has a specific definition, any single member LLC where that member lives in California qualifies.