How to write unit test for my tagless algebra?

I have an interpreter for an algebra and I would like to write a unit test for it.

The interpreter is as follows:

final case class LiveDbConnector[F[_] : MonadError[*[_], Throwable]](env: Environment[F]) extends DbConnector[F] {
  override def read(url: DbUrl, user: DbUser, pw: DbPw): F[DbParams] =
    (for {
      a <- OptionT(env.get(EnvVariable(url.v)))
      b <- OptionT(env.get(EnvVariable(user.v)))
      c <- OptionT(env.get(EnvVariable(pw.v)))
    } yield DbParams(DbUrl(a.v), DbUser(b.v), DbPw(c.v)))
      .value
      .flatMap {
        case Some(v) => v.pure[F]
        case None => DbSettingError.raiseError[F, DbParams]
      }
}

the algebra is as follows:

trait DbConnector[F[_]] {
  def read(url: DbUrl, user: DbUser, pw: DbPw): F[DbParams]
}

the implementation is as follows:

final case class DbParams(url: DbUrl, user: DbUser, pw: DbPw)

object DbConnector {

  def impl[F[_] : MonadError[*[_], Throwable]](env: Environment[F])
  : DbConnector[F] =
    new LiveDbConnector[F](env)

} 

I use the test framework https://scalameta.org/munit/.

How to write unit test for my above algebra?