Agentic IDEs/extensions usually continue the conversation until the context gets close to 80% full, then do the compacting. With both Codex and Claude Code you can actually observe that happening.

That said I find that in practice, Codex performance degrades significantly long before it comes to the point of automated compaction - and AFAIK there's no way to trigger it manually. Claude, on the other hand, has a command for to force compacting, but at the same time I rarely use it because it's so good at managing it by itself.

As far as multiple conversations, you can tell the model to update AGENTS.md (or CLAUDE.md or whatever is in their context by default) with things it needs to remember.