I am concerned about this too. On my OnePlus 8T I can apply some tweaks to enable VOLTE on Digi. But Pixel seems harder.
But this is the same for some brands like OnePlus too, until today no VOLTE out of the box.

Does anyone know what will happen?

Ok I just did some research, apparently 2G network is still going to stay (probably due to lack of 4G penetration in rural areas and for emergency calls).

So if all 3G network is shut down, without VOLTE we will fall back to 2G which doesn't come with HD quality calls.

For current Pixel phones, there's some mods available (no root needed) to enable VOLTE if you have a config file called MBN, rather technical but at least possible. But that process only works for Qualcomm SoC. With Pixel 6 using Google's own Tensor SoC, it might not be possible

I am not using P6 but OnePlus 8T with AOSP Android 13 ROM. My experience with the following works in both AOSP and OxygenOS, so I guess it should work for P6 too. Even the notorious Citibank can bypass.
1. Latest magisk
2. Zygisk enabled
3. Latest shamiko module
4. Latest universal safetynet fix module by kdrag0n
4. Configure the DenyList, make sure all the sub modules of the app are checked.
5. Since you use Shamiko, DenyList should be *disabled* (not enforced). Shamiko will read the DenyList instead.
6. Make sure there is NOT a single file in your internal storage (internal SD) has the name "magisk". << Some apps like citibank detects this.
7. Use the built in magisk function to rename magisk to other name e.g. Manager or anything