That is much more than a grout problem; you've got a supply line leak.

Start with a plumber to check the plumbing between the valve and showerhead. That's the most likely problem.

Once the leak is handled, worth replacing the grout in the corners with silicone. That will allow some movement between the walls without cracking.

Grout cracking in corners is inevitable. That's why the industry standard is color matched silicone instead of grout at changes of plane (e.g., corners). But grout is not waterproof, so -- even if it's cracked -- it shouldn't be the reason for a leak...if the walls were properly waterproofed. As suggested above, you may have a plumbing leak inside the wall. Can the wall be accessed from the backside? If not, the tile may have to be ripped out to get at the leak.

Perhaps you might find this resource helpful from the National Tile Contractor's Association: https://cdn.ymaws.com/www.tile-assn.com/resource/resmgr/docs/help!_my_shower_is_leaking.pdf

Hopefully the wall can be opened from the other side. It will make it easier to find the source of the water leak. And to reiterate others, there should not have been grout in that corner; it should have been silicone. In your case maybe you were lucky to have it happen this way , otherwise you might not have found that water leak for a while.

Good luck!