Baby sleep question – when to start sleep training & which method?

My son is almost 6 months old, exclusively breastfed.

Sleep habits:

Only falls asleep while breastfeeding/rocking. Needs me nearby.

Wakes ~45 min after bedtime, then roughly every hour overnight, needs breast to resettle. Sometimes wakes fully and wants to play.

Naps:

Very inconsistent. Most ~45 min (sometimes only 20 min if put down). Contact naps can extend up to ~1h15min.

Wake windows:

Usually 1.5 h or less. Recently sometimes up to 4 h in the morning (doesn’t make sense).

Routine:

No fixed bedtime or routine except diaper + sleep sack. I usually sing while breastfeeding/rocking. Bedtime based on wake windows, naps, and morning wake-up.

Teething:

Teething since 3.5 months. Bottom teeth at 4 months, top incisors at 5 months. Now upper lateral incisors are coming. Almost always unsettled.

Question:

Given his age, teething, short wake windows, strong sleep associations, and exclusive breastfeeding:

When (or if) to start sleep training?

Which method might be suitable?