A display repair can be carried out via Digitec, but on 08.07.2022 I received a repair estimate of CHF 518 from the service centre. This means that the repair is hardly worth it, as the new price is only slightly higher.
However, I also recommend a repair with a cheaper provider or, as already suggested, an official repair kit with video instructions via ifixit...

I haven't used this myself yet, but you can also register your Pixel 6 for repair in the menu under "Returns, repairs and support". I don't know whether they can actually offer you a repair.

I had the display of my Pixel 6 replaced by an external provider (nanorepair.ch).
Alternatively, you can now buy official repair kits for Pixel phones, among others, to get started yourself: https://store.ifixit.de/collection...