Possible cost overrun

Really? A cost estimate just means that preliminary cost estimates exist. It does not mean that there are absolutely fixed prices.

That's exactly right. Despite quotes, the amount can still be charged if positions that are mandatory were not priced.

There is a cost estimate, basically like here "costs approx. 2000€/m²", then the calculation "quantities calculated and price assumptions" and then the cost proposal "quantities with actual prices". After that comes only the cost determination (explains itself). If there are dramatic price changes after the cost proposal, either someone botched it or the client has new wishes. Otherwise, there is no reason for it.

If there are dramatic price changes after the cost estimate, either someone messed up or the client has new requests. Otherwise, there is no reason for it.

Hehe, in recent years I have NOT seen a single project that actually stayed within the budget for all items. And my clients are professionals, not amateurs like us private home builders.

Yes, people make mistakes, some more, some less. With us, the cost estimates matched the final invoice quite accurately.

Actually, we think that once the offers have been obtained, we have a price guarantee, right?

Who is supposed to give the guarantee anyway?

We have also stayed very close to the offers... so it works.

Many offers have something like "we consider ourselves bound to the offer for xy months/weeks" written on them.

In my opinion, a conversation with the architect is due now to find out why the prices (all?) are (significantly?) higher than his estimate.