Deployers can ssh to all mw hosts (appservers, api-appservers, maintenance, jobrunners, etc.) to e.g. run scap pull or another one of a narrow set of commands during investigations.
But, they can't ssh to any of the parse* hosts because they don't seem to inherit or or otherwise have set the standard set of appserver-ish admin_groups.
I don't know if there are plans for, or decisions made against, having parsoid be a role within the mediawiki:: hierarchy. But in the interim perhaps it would make sense to add these two groups (deployers and perf-roots) to the parsoid role.
https://wikitech.wikimedia.org/wiki/Incident_documentation/2021-09-01_partial_parsoid_outage