I'm with Krissie put another piece of moulding over it. Perhaps a 14/ round piece added to the top of the door. If this is an aesthetic repair, IMHO filling a gap like that with flexible caulking won't look good. That being said, if it's not aesthetic (you can't see it normally but need to get on a tool or something to see the top of the soor frame) then what difference does it make? Leave it and forget about it. Lastly, you could remove the top molding, cut out a piece of the drywall and replace with a piece that will fit nicely to the frame, finish the drywall joints, paint the wall and replace the molding. "filler" is not a good solution. Just my 0.02.

Yes there should something to cover that area because if your tiles do not cover the the window will not look good and the finishing will not be neat and proper.

OMG their workmanship is terrible. Obviously you didn't have a permit, because no City would have approved this job. You need to cut your losses and have this redone by a professional tile person. You should NOT under any circumstances be giving them advise on how to fix this. You will be giving them an out, because all they need to say is "She told us how to do this and we were just following what SHE wanted. SHE knew we weren't tile professionals. What you are seeing is just the tip of the ice berg of problems. I agree that probably the drainage of the floor is probably also wrong. Did they also do the Plumbing as well? In the future, you will undoubtedly be faced with major water damage to your home. If any damages occur down the road, it may be difficult to get your insurance company to pay for repairs once they see how this was done. These people need to return your money and the cost of your tile so you can redo the shower. For goodness sake don't let them work on any thing else in your house. If you need references, I would go to a large reputable tile store and ask them for people they know and trust. Be sure to check that their license. You can do this by checking their license no. with your State's Contractor's Board. Best of Luck to you.

It wasn't his cabinet maker, we hired him, but he and his finish carpenter thought about adding mdf on the back and sides of the space to cover the gaps and then painting it the color of our walls. It's an idea but we know that it's going to end up being around $1000. And with the cost of building a house in these times, ugh, we just don't want to pay that. We thought about shiplap but it's a Prairie Modern house and it just doesn't fit.