Introduce ::Zoekt::Logger and log search errors

What does this MR do and why?

Zoekt is a new code search engine we recently integrated in !105049 (merged). This MR adds special logging for it in a new zoekt.log file.

Screenshots or screen recordings

{"severity":"ERROR","time":"2023-02-03T03:51:53.847Z","correlation_id":"01GRAPDWJXG27ZXPDN0885PDQ8","message":"Zoekt search failed","status":400,"response":"{\"Error\":\"error parsing regexp: missing closing ): `hello(world`\"}\n"}

The corresponding change in fluentd should be merged once after this gitlab-cookbooks/gitlab_fluentd!271 (closed)

How to set up and validate locally

Setup instructions can be found at !105049 (merged) and triggering this failure can be done with any invalid search like hello(world (as this is an invalid regex).

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.

Related to #390001 (closed)