Right. PE is a pure price measure. It is the theoretical price of $1 of theoretical earnings. It's really a sentiment measure, because the buyer of that dollar of earnings has no claim on it whatsoever. Stocks have no more value than bitcoin. Their worth to the owner is what someone will pay them for it when they want to sell it.
Stock prices are figments of traders' imaginations based on how much cash they have in their pockets. And over the past dozen years that's been most heavily determined by how much cash the Fed wanted to give them.