Migrate or shim BBE logger arguments to `slog`

[nadiamoe]

In https://redirect.github.com/prometheus/blackbox_exporter/pull/1311, BBE switched to slog, and that is blocking us from upgrading it:

Run make build-native
Building github.com/grafana/synthetic-monitoring-agent/cmd/synthetic-monitoring-agent (linux-amd64)
# github.com/grafana/synthetic-monitoring-agent/internal/prober/grpc
internal/prober/grpc/grpc.go:46:62: cannot use logger (variable of interface type logger.Logger) as *slog.Logger value in argument to bbeprober.ProbeGRPC
# github.com/grafana/synthetic-monitoring-agent/internal/prober/tcp
internal/prober/tcp/tcp.go:46:61: cannot use logger (variable of interface type logger.Logger) as *slog.Logger value in argument to bbeprober.ProbeTCP
# github.com/grafana/synthetic-monitoring-agent/internal/prober/http
internal/prober/http/http.go:65:62: cannot use logger (variable of interface type logger.Logger) as *slog.Logger value in argument to bbeprober.ProbeHTTP
make: *** [/__w/synthetic-monitoring-agent/synthetic-monitoring-agent/scripts/make/build.mk:21: build-go-linux-amd64-github.com/grafana/synthetic-monitoring-agent/cmd/synthetic-monitoring-agent] Error 1
Error: Process completed with exit code 2.

We should either move to slog, or somehow shim our existing logger into slog for BBE to accept it.