Is there a limit to the number of codex entries/chats/snippets I can have?

There are no limits, and you can have as many in as you want.

If you have thousands of chats/snippets/codex entries, and then open everything on an old phone/device, you may find that it crashes, but the only real limit is the hardware (i.e. we haven’t set an internal limit to the number you can have).