This is an example of how Discovery got worse over the seasons.
In S01E03 they did send the away team in tactical gear and with at least one security officer over to the USS Glenn.
They used the tactical gear in S1-S3 a lot.
Why was the communications officer and the tactical officer on the team? (Token screen time for the characters out of pity?)
Why was the away team not in 32nd-century tactical gear?
It is as if the mission was destined to fail, so no point in making 32nd-century tactical gear for the characters.
I have my own little theory:
Did you notice something about that away team?
All male.
They all had to be rescued by Michael Burnham and the (almost) all-female bridge team.
The men are falling over each other and on their knees in front of women.
Men prostrating towards Michael Burnham.
When Michael Burnham, said that she wouldn't lead the boarding team, that wasn't a smart command decision, that was part of the setup.
The boarding mission was destined to fail, and Michael Burnham can't fail! (unless it's a Xanatos gambit, like in S04E08)