Count the X fetches each bot pass spends #500

The climb raised the ceiling for one mention from 3 fetches (the post, its parent, the chase) to 5 (the post, three parents, the chase), and nothing counts what a pass spends, so the shared syndication budget is read only from upstream failures. Add a fetch counter to the pass summary (bot.py), beside the reply-budget counts, and read it before _BARE_TAG_MAX_CLIMB is tuned again.

Imported from planning/backlog.md.