We got a new toilet installed and the next morning, there was water pouring into the room below from the ceiling. The thing is, the water started pouring down when the shower ran. Note that this was the first shower after the toilet was installed. We flushed the toilet many times throughout the night and saw no sign of leak. Did notice that there was some gunk/hair coming up in the shower. Still waiting for a plumber to come by to figure out what is going on. (Added note - the toilet did clog a few times in the weeks before the new toilet install. Also, the day of the install - after I think - I noticed that when I flushed the toilet, the shower made a gurgling sound. Toilet has not been clogged though. It is flushing fine.)
QUESTION - Is there any way the toilet install could be "connected"? I have no clue but it seems more like a clog or pipe issue vs. a problem with how they installed the toilet...
Typically the shower drain will join the toilet drain pipe under the bathroom floor. Perhaps the toilet installation caused the shower drain pipe to crack or separate by moving or shaking the pipes or perhaps a screw was driven through the shower drain pipe. It's possible this would happen in a way that leaks only from the shower and not from the toilet.
It could be a coincidence. Perhaps the shower drain cracked or broke at this time coincidentally, or it was already cracked or broken (or an old glue joint wasn't glued) and the toilet installation just did something that made it start leaking.
Either way, in my opinion, the easiest way to diagnose and repair this is to break open the ceiling in the room below. It's soaking wet and ought to be replaced anyway, it will give you access and visibility to the problem, make it easy to fix, and allow the joists to dry. If the ceiling is drywayll just get a hand drywall saw and start cutting where the water is coming through.