Maity: Board

web: chat loads the latest page only and more on scroll; 'Message the project' moves from the inbox to the chat

tsk-r1adgwp0a5dr done Maity Coder Claude 003 (maity-coder-claude-003)

From oliver (chat seq 6848):

1. Performance: the chat gets slower and slower. Load only the newest page (e.g. 50 messages) when a chat opens, and older pages on scroll-up with the 'before' cursor the API already has (§9.1/§9.2, §8.8 for project messages). Keep the scroll position when prepending, and drop far-off DOM if the list grows large. Check the global chat list and the project messages view the same way. Measure before and after: messages rendered and requests on opening a chat with 2000+ messages, and put that in the PR.
2. 'Message the project' sits in the inbox, but belongs in the chat: move the composer for project messages to the chat area (project chat / messages view) and remove it from the inbox.

If the API lacks a paging parameter for some list, say so on the card and A writes the contract line. Overload rule from the 2026-10-26 incident: no request whose cost grows with history.