Learn German: Seit der Krise gewinnt die Frage an Bedeutung. - Since the crisis the question has gained in importance.

In German, when a situation starts in the past and continues into the present, you use the present tense combined with seit. English requires the present perfect ('has gained') or present perfect continuous ('has been gaining') for this. Because the effect of the crisis is ongoing and the question is still gaining importance, German uses the present tense.

How does an Bedeutung gewinnen fit into the idea of perspective shifts in support verb constructions?

an Bedeutung gewinnen (to gain importance) represents the intransitive perspective, where a process happens to the subject naturally (die Frage). If you want to shift the perspective to an active agent who intentionally makes the question important, you would use a transitive construction like der Frage Bedeutung beimessen (to attach importance to the question).

Why do we use the preposition an here, and what case does it take?

The fixed phrase an etwas gewinnen means 'to gain in something' (like size, speed, or importance). Here, an takes the dative case. You do not see the dative marker on Bedeutung because there is no article, but you would see it clearly if you added an adjective (for example, an großer Bedeutung gewinnen).

What is the direct opposite of this support verb construction?

To say something loses importance, you simply swap the verb but keep the exact same prepositional structure: an Bedeutung verlieren. Both are highly common fixed expressions in written German and news media.