No, the problem would NOT persist with the engine off. Any manual tranny will let you shift without even using the clutch if the engine is off. (Occasionally, it might be slightly difficult in a particular gear because gear teeth are tooth-to-tooth…not meshing. But otherwise, you can shift freely.) If your system is not fully bled, it is just like you are not getting the clutch fully pushed down. Any manual car will show difficulty if the clutch is not fully pressed.
The warm engine might allow some expansion to slightly alleviate the problem, but my guess is that even then, as you let the clutch out very slowly, you will find the engagement point is too near the floor. You might even feel some drag even if the clutch is floored…tending to move the car forward.
Take it back to the shop before you damage the first gear synchronizer in the tranny.
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