After 15.6 update cannot connect to carrier

Try first to optimize the range of the mobile network, see this Apple article:

If you see No Service or Searching on your iPhone or iPad

If you see No Service or Searching on your iPhone or iPad - Apple Support

See also these Apple articles below:

Manually update your carrier settings on your iPhone or iPad

Manually update your carrier settings on your iPhone or iPad - Apple Support

Update your network provider settings manually on your iPhone or iPad

Update your network provider settings manually on your iPhone or iPad – Apple Support (UK) 

If you can't make or receive calls on your iPhone

If you can't make or receive calls on your iPhone - Apple Support

Please see again: If you can't make or receive calls on your iPhone

If you can't make or receive calls on your iPhone - Apple Support

👉  Contact your carrier

When you contact your carrier, make sure that:

• Your account is set up to use your iPhone.
• There aren't any localized service outages.
• Your account doesn't have a billing-related block.
• Your calls don't have errors on the carrier system.

👉 Contact Apple Support

If you still can't make or receive calls, contact Apple Support, then follow the steps to complete your request.

Also contacted my carrier but they insist that everything is ok on their side.

Visit them, maybe the SIM card is damaged, ask for a replaced (new) card. Normally it is free.

Check if the SIM tray is bent, as even a tiny misalignment can cause the SIM card to not fully connect with the internal contacts in your iPhone.

As to Apple support, it sent me to this forum.

No, you are not sent to this forum.

This is what i get here: