Allow Slack bots to trigger Claude Tag

Claude Tag currently only responds to human users tagging @Claude in Slack. It would be useful to allow other Slack bots to trigger Claude Tag too.

Use case: automating workflows where a bot (e.g. a CI bot, monitoring bot, or custom integration) tags Claude in a channel to kick off a task, like triaging an alert, summarizing a thread, or running a code review.

Right now there's no way to programmatically start a Claude Tag session from another bot. Supporting bot-initiated mentions would unlock a lot of automation on top of Claude Tag without needing a separate API.