See PHI225. Previously, see D15335 / T10413. On workboards, we hide archived project tags since they aren't terribly useful in that context, at least most of the time. Originally, see T10349#159916 and D15297.
However, hovercards reuse this display logic, and it's inconsistent/confusing to hide them there, since the actual "Tags" elements on task pages show them. Narrow the scope of this rule.