I don't want to dampen any hope that the previous poster may give you, but I didn't sleep train (we tried briefly at 6.months and again at a year, but my husband couldn't bear it and my son is a child of stongly held opinions like his father!) He's now 3 and still sleeps dreadfully through the night, needs someone whenever he wakes up, my husband regularly has to spend 1 hr or more in the room with him in the evening. I also have a 11 month old who is also breastfed and a not great sleeper, following a common pattern much like yours. He's not sleep trained either and I have had to cope doing everything on my own for him over this first year becsuse of the support tueneldest needs, and it has been very hard.*
If I had my time again I would have sleep trained the eldest: a) because I didn't think about the ramifications of what you do with the first on the second child- hasn't been able to have the early bond with his father, but having wanted to treat both the same so don't feel i should sleep train second either and b) despite inveitable setbacks (teething, illness etc) thar occur even with sleep training, I now firmly believe the long term being able to teach a child how to sleep well and independently is invaluable for their health and development and the parents.
Anecdotally my friends who sleep trained have MUCH better sleeping toddlers now, and I feel sometimes wlthat we have done a disservice to our child who needs so much more support and is forever in cycles of waking up too early, tired all day, grumpy, shifting bedtimes and naps.
Also one tbing I didn't properly take on board, but I firmly believe: the later you leave it the harder it will be. Imo 8/9 months may be the sweet spot.
But I didn't manage it, so no judgement from me! Also I know that's totally not answering the question you asked but I just felt it might be useful to know our experience in case it goes the same way for you (to prepare yourself!)
*fyi for context no medical or weight issues in either child, they are thriving otherwise and are both very clever active boys ahead on all milestones.
Good luck to you xx