ChatGPT/Codex is equally bad (if not worse). Which is very surprising. Indexing words is a solved problem. It would be trivially easy to provide a useful semantic search. I can only surmise that they prefer people start new chats instead of re-opening old chats.

The best way around this is a project folder like "Personal" or something contextual, then getting Claude to record everything into md files with semantic indexing. It doesn't require too much space. Just a little background processing.