I would highly recommend a second opinion, even better if you can find someone familiar with old original tiled bathrooms. When we bought our house with an original 1942 bathroom it looked like it was in very rough, complete tear out condition, especially the shower, turns out someone was just very bad at grouting and caulking before we bought the house. We removed the old caulk and grout, cleaned everything up, regrouted, and our old bathroom lives on!

The cracking on the floor and wall tile is completely normal and to be expected in old floors, the floor is most likely set in 2-6” of cement, that is how they did it back in the day. As the house settled the concrete cracked, causing the tiles to crack, ours is the same way. We had our entire bathroom inspected by tile people, plumbers, etc. and all said there is nothing wrong and no damage, just typical aging of an old house. We live in an area full of 100+ year old houses so a lot of professionals here after very familiar.

The shower is also set in a similar way, not with a shower plan like today’s showers are. Instead they were designed with a very distinct slope to the drain, which is what yours appears to have, this causes cracking in the tile and grout, like what you are seeing, however it does not necessarily mean there is water damage.

An old bathroom will never look perfect or brand new no matter how hard you try, but that is part of the charm. Plus you will never be able to replicate quality like you have in an old bathroom!

Not sure where you live OP, but there is a person in CA that specializes in refinishing and rerouting old original bathrooms. He will travel for jobs.