Claude Code (via the subscription) will continue working under Paseo but it will consume a different pool of credits, which depending on your sub you get different amounts. Practically speaking you will be able to use only a fraction of your usage in Paseo, this applies to any programmatic usage of Claude Code.
This might help: https://support.claude.com/en/articles/15036540-use-the-clau...
Paseo has a terminal if you want to keep using the TUI inside of it, works on mobile and desktop.
I will keep supporting the Claude Code harness in Paseo, as many users are using it via direct API usage and sometimes even with Chinese models.