We are planning to build in 2022; the planning begins

It will also depend on the bank. A local bank will react differently than a large online bank with standardized processing

If we choose a general contractor and then sign a contract, what is the sequence until you apply for financing? You have to know all the costs first, or can I give the bank approximate values?

A construction contract is not a letter of intent, but already a binding order - you will no longer be able to get out of such a contract without compensation. So you should have the financier on board for the budget before signing. The person handling this at your bank is not the same who handles the loan for your car or washing machine - but someone who knows about home financing. That means they generally also know that costs cannot be estimated down to the gram; and if it is a bank from the region, they also know the authentic price level. So you should no longer make any changes in terms of scope and level.

My question was whether I can also submit estimates as total financing.

It is not about me not getting financing.

I understood and answered that: you never know the costs exactly in advance. You asked about the order, and it must be: first have money, then enter into commitments.