I know there's the 'Away Team' game but I think that's all just ground exploration.

The SNES 'Next Generation' is a good but very lackluster and crude example.

Looking for what Space Crew is but more serious, less cartoony, and less focus on ship maintenance (although some is fine)

The old Interplay adventures 25th anniversary and Judgment rites feature both space combat and ground missions (point and click adventure).
I believe A final unity for the TNG era is similar. Also Generations. But I haven't played those two myself.

Thanks for the references

Sadly TNG is point n click on ground and Generations is point n click flying. lol

I should say kudos to the developers of TNG for adding in SEGA (Arcade) space combat.

Star Trek Online.

Ground gameplay is... fairly standard MMO, but the space sections are like a simplified Starfleet Command with the ability to move up and down added.