[atn18]

Description of changes

• A message sent while a long update handler was running waited in grammY's sequential update loop. When it was finally handled, the stale check (older than 60 seconds) dropped it and sent "Some messages were skipped while Telegram was unreachable" - although Telegram had delivered the message and the bot was simply busy.
• After 5 seconds without chat output the bot now tells the chat it is busy, so the user does not resend into the silence. While the chat keeps receiving progress (for example a session-pick transcript, streaming drafts or edits) the notice waits, and it is re-checked once the chat goes silent.
• Messages delayed by a long handler are executed after it within 15 seconds; older ones are dropped with a separate honest "the bot was busy" notice. Messages delayed without a busy window keep the existing outage behavior and text.
• Busy windows are only recorded for handlers that actually ran: an update dropped by the stale check never starts a busy timer.

Closes issue (optional)

• None

How it was tested

• npm run lint, npm run build, npm run typecheck, npm test - all green (2825 passed, 7 skipped).
• New tests: busy-window recording and boundaries (second rounding, TTL, windows kept until the TTL, 14-second recording threshold); the measuring middleware records long handlers, ignores short ones, records when the handler throws, sends the busy notice once after 5 silent seconds, waits while the chat shows progress and re-checks once it stops, and logs a failed notice send without failing the handler; a message delayed by a busy handler within 15 seconds runs, past 15 seconds is dropped with the busy notice, an old message covered by a busy window prefers the busy notice over the outage one, a transport delay without a window runs, and an outage keeps the outage notice; draft sends update the chat-activity timestamp; a mixed burst queues both notices one second apart.
• PRODUCT.md updated with the two-stage behavior.

Checklist

• PR title follows Conventional Commits: <type>(<scope>)?: <description>
• This PR contains one logically complete change
• Branch is rebased on the latest main
• I ran npm run lint, npm run build, and npm test
• If this PR is OS-sensitive, behavior/limitations for Linux/macOS/Windows are described