The architect is wrong with the estimates. And now?

That is the risk when relying on estimates rather than actual quotes for financial calculations.

I experienced this myself with my ex. The costs were also estimated (engineering firm), and when the quotes arrived, there was a rude awakening. Only one company wanted the contract, and their price was significantly above the estimate for that item. During renegotiations, a discount was agreed upon. That was already in 2006, so it is not a new development.

And when was the architect's calculation? Keep in mind, the billing according to HOAI is based on his calculation, right? If he had calculated 400,000 instead of 300,000, you would also have to pay the architect 1/4 more, wouldn't you?

The basis for calculating the fee usually depends on the construction phase. Up to the building application, the fee is based on the cost estimate. Once the trades are awarded, it is based on the actual costs. The architect himself will probably become more expensive again during construction supervision. Better check the contract again to see how it is regulated in your case.

The basis for calculating the fee usually depends on the construction phase.

That is not correct, the basis is always the cost calculation. Since follow-up invoices are issued, the fee can change over the phases. For example, the preliminary planning can have been billed based on the cost estimate; if the cost calculation is then higher, the fee for the preliminary planning is also adjusted. If he wants to enforce the cost determination in a way that affects the fee, they usually meet in court.

That is not correct, the basis is always the cost calculation. Since follow-up invoices are issued, the fee can change over the phases.
For example, the preliminary planning may have been billed based on the cost estimate; if the cost calculation is then higher, the fee for the preliminary planning is also adjusted. If he wants to enforce the cost determination with a fee effect, they usually meet in court.

It is actually contractually regulated that way with us, as I wrote. Nothing is recalculated afterwards; we agreed on that in advance, or it is customary with our architect and was already in his contract template.
That is also why I advised the original poster to review their contract again.

That is why my advice is for the OP to review their contract again.

And what if there is no clause regarding that?

Was the architect contract concluded as a contract for work? If yes, it can be briefly said that the architect owes a successful result. There are relevant court rulings in which the architect had to return all payments made to him to the client due to budget overruns. His work performed was therefore not compensated due to the defect. If you want to go this route, get advice from a lawyer...

An agreement and a nice gesture from the architect would be to at least waive any potential higher fee from the cost overrun. One certainly must not overlook that the market is currently "crazy" and many experiences from the past decades are no longer valid.