Doobie LogHandler dont work with a quill

[apavlychev]

Version: 4.8.1
Module: quill-doobie
Database: postgres

Expected behavior

A effectfull logger LogHandler (https://tpolecat.github.io/doobie/docs/10-Logging.html) work with a quill

Actual behavior and steps to reproduce the behavior

I've seen the logger work only when I have a doobie statement:

import doobie.implicits._
sql"SELECT 1".query[Int].unique.transact(transactor).unsafeRunSync()

and don't work with quill:

val doobieContext = new CustomPostgresContext(SnakeCase)
import doobieContext._
import doobieContext.compat._
import doobie.implicits._
run(quote(qsql"""SELECT 2""".as[Query[Int]])).map(_.head).transact(transactor).unsafeRunSync()

@getquill/maintainers