Use the Sentry Nuxt module instead of our temporary implementation

[obulat]

Problem

The Sentry module for Nuxt 3 is in Beta stage now. It is better to use it instead of the current implementation.

Edit: I tried the new module locally, and it can't build due to getsentry/sentry-javascript#14671. Blocked until that issue is fixed.

Description

Add Sentry module according to the instructions in the docs. Set up client, server and source map uploading.

Alternatives

Keep using the current setup. We cannot see the source map currently.

Additional context

When migrating to Nuxt 3, the Sentry module for Nuxt 3 wasn't released yet.