If you can approximate the location of the studs, depending on the size of the joints, you could probe the wall through the grout joints which would be an easy repair.
There are higher power stud finders that I thought would read through 1-1/4” but I’m not sure if that’s through tile or just drywall.
If you were able to access the back of the wall, I would prefer to open that up and install blocking rather than rely on hitting the studs.
Just googled no drill grab bars and found this.
https://www.nodrillingrequired.com/GRIPP-Series-Mounting-Hardware-p/gb00002-ndr.htm