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I get that it counts as th unit having psychic mastery lol one, but can the unit generate their own psychic powers and have access to the primaris power? For example, would a grey knight strike squad be able to do all of the things a plain SM librarian would be able to do?

No because their profile just states what power they have

The mastery level depends on the codex entry. For example, Purifiers are Mastery Level 2 despite being a Brotherhood of Psykers.

Brotherhoods generate powers like a normal psyker. But some psykers (most Grey Knight units) come with their powers pre-selected.

So your Strike Squads have Hammerhand and Banishment already selected in their entry, thus they do not roll for powers because they're already maxed on powers.

And I'm sure in the rulebook it says when you role all your powers on a certain table you get the primaris power, but as a srikesquad makes no roles they dont fall under the rule of getting it

 total0 wrote:
And I'm sure in the rulebook it says when you role all your powers on a certain table you get the primaris power, but as a srikesquad makes no roles they dont fall under the rule of getting it

Fortunately they thought about this in the Grey Knights codex because whenever they give a unit a power they also gave them the primaris power (Banishment).