No: Teams does not support hashtags, at least not yet, in a way Twitter or Yammer uses them.
Yes: You can use hashtags, but you need to put some personal effort there (agreed) hashtags.
How: add desired hashtags to content so you can use these hashtags in search. You can add them to discussions, OneNotes or inside documents too (if you so wish to – but usually just include the document in Teams discussion and use hashtag in there).
Why: Hashtags can combine information from different topics and teams into one search result. You can even use these in private chats.
No: It won’t show you anything from any team you are not member of. And it won’t return any results from private chats unless you are a chat participant It does not search inside calendar meetings.
Benefit: You can find some content, like chats, using hashtags in search.
As we all know Team’s search needs improvements – however with hashtags the search works really nicely. Of course if you can use Microsoft Search then the results are nicely in one view.
The drawback: you need to use same hashtags as everyone else. If you stick to few well known topics (#Microsoft365, #ProjectName, #HRNews) that can help surfacing some information.