13,000 to renew old shower and bathtub?

Of course the services rendered will be paid for, but the follow-up order does not have to be placed; my basic question is whether this is normal or if I should better hire another company for the remaining work

I understood it as if the company is already in the middle of their work.
What the "right" decision is cannot be told to you here, as it depends on many factors.
If you go with this company, it is certainly the easiest, but apparently very expensive. Do you get annoyed afterwards about the high cost or possibly mediocre service, or do you simply let it go and are glad that it is all over; everyone is different in that regard.
You can already recognize my approach from my previous words, yet I also cannot tell you how things will continue afterwards.
I don’t like such matters at all and feel poorly treated as a customer, which is why I am willing to endure the consequences of a corresponding decision against it if necessary, even though it doesn’t always get easier. However, through these "detours" I have repeatedly met craftsmen with whom I still gladly work today.

Keep us updated. I always find something like this interesting and especially helpful for builders. And don’t worry: Everyone here has messed up things during construction that they would like to do differently in the future.

my fundamental question is whether this is normal or if I should better hire another company for the remaining work

Then answer the questions posed to you.

Then answer the questions directed at you.

"Wow, thanks for your enlightening words – too bad they don’t help anyone. But hey, at least you got to feel important for a moment. Maybe next time it will even work out with some content."

Keep us updated. I always find such things interesting and especially helpful for builders. And don't worry: Everyone here has messed up things during construction that they would like to do differently in the future.

I have decided to put the work on hold for now until I have obtained a second cost estimate from another company. My research has shown that this task usually costs between €3500-5000; since my bathroom is not large, I will take the middle as a guideline, then the invoice would be three times as high... That is crazy!! I will gladly get back to you with the result!!

Just by the way. Have you reported the water damage to the insurance? Does the contractor know that too? Back then I had ordered a leak detector from the insurance. Did they call out the prices there? For example, a construction dryer for 300 euros / week.