Downtime is not an issue for me.
Two apps I think of, would be - virtually identical - but not the same.
Two apps would be different sites, meaning, different dbs, volumes, ports, names… but they would have the same - so to speak - base discourse (+ same plugins, same whatever might critical to that core/base).
In ideal world of Discourse - if such does not exit yet - for such scenario, such new image once build first/one time, could be used even with docker tools directly - and DB or anything what would have to be “migrated” to such new image/discourse version, start/boot process of such “secondary” container would - perhaps with help of env vars - decide to check/carry out necessary migrations of dbs.
Main advantage - which many must have thought already of - is a single image for both (or many more if some people do that) containers/apps.