How does sorrel come back every year if you pick it all, when people say it's an annual?
Some things are annuals in some places (usually colder) and perennials in other places. And some people say things that are not strictly true. Tomatoes are perennials - in the tropics, or in a heated greenhouse. But we treat them as annuals in the colder regions, normally.
I find "French sorrel" to be an unreliable perennial in my garden - I will get a few survivors, but they don't all survive. French tarragon is similar, though actually better at surviving in general for me.
A seed company describes it as a perennial, but also says zone 6-10, so not surprising that it expires in zone 4/5 many times. Much permaculture literature is from balmy climes, I have noticed.
Some are annuals that reliably self-seed.
Wood sorrel is one of those, and has largely taken over the "sorrel" role for me as a result. I don't use a huge amount of it and have so far not been noticeably impacted by its oxalic acid content (which regular French sorrel has as well, I note the seed company claimed theirs had been bred for "low oxalic acid content" though I don't know what the relative amounts might be.