Function live_activity 

pub fn live_activity(pool: &DbPool, limit: i64) -> LiveActivityDto

Gathers the LiveActivityDto over one pooled connection. Like admin_status, every read is best-effort (degrades to an empty list) and read-only — the dispatcher is never involved, so the live feed cannot perturb the conversion hot path.

The feed is conditioned on the active run’s service — the one actually generating messages now (the latest HistoricalRun). A co-resident legacy service (e.g. a Perl tex-to-html sharing the DB with the Rust oxidized_tex_to_html run) therefore never pollutes the live view; the feed follows whatever is converting. With no runs yet, the feed is simply empty.