Can the Imperial player use the Heavy Troopers from Twin Shadows (as an example of a non-unique group) as an open group in a core game campaign mission, or are they prohibited under the 'Component Limitations' rule?

Yep, any non-unique deployment cards can be used in any mission, although pay attention to any environmental restrictions, e.g. Wampas need snow.

"Heavy Stormtrooper" is not a "Stormtrooper" group, their own limits do not affect each other.

You can have up to two regular Stormtrooper groups, one elite Stormtrooper group, one regular and one elite Heavy Stormtrooper group in a mission (between initial, reserved, and open groups).

https://boardgamegeek.com/thread/1948107/using-open-groups-expansions-core-game-campaign