I had this happen to me with an 86 Toyota Tercel 4wd. The threaded rod goes through the inner race of the bearing in the strut mount. The outer race is bonded to rubber. The rubber can crack horizontally, actually kind of cone shaped.
The strut did not fall out until I disconnected the strut from the steering knuckle. I expected the strut to hang from the upper strut mount, instead it just fell down onto the ground.
If in your case, the strut did not come out until it was disconnected from the steering knuckle and the mechanic put everything back, it might be safe to drive around town. The rubber block had to have been broken before the mechanic worked on it just as mine was broken before I worked on mine. As long as we didn’t know, we didn’t have a problem driving the car.
While that makes logical sense to me, I got a new strut mounts and struts and did not drive the car until I replaced them. So if you don’t want to drive it either, I don’t blame you.
About 1/2 way down the page are pictures of my broken strut mount