I also had this with my third baby. It was a bit of a surprise as he only turned breech at 36 weeks after previously being head down. I was offered an ECV and of the three options (Vaginal breech birth/ECV/planned c-section) I knew that I absolutely didn't want a vaginal breech birth, and a planned c-section would have been OK, but I was hoping for a straightforward vaginal birth, so ECV made the most sense to me. I had a look at the other methods to try to persuade the baby to turn (e.g. Spinning babies, moxibustion) and it sounded like the evidence for them wasn't very good so I didn't see the point in bothering with those. I felt like if I was going to try and persuade him to turn, we might as well go with the nuclear option!
I was told that it had a small risk of putting the baby into distress resulting in me needing an emergency c-section immediately under general anaesthetic. I was a bit nervous about this risk, but it was fairly small, I've had a GA before so wasn't nervous about that. It seemed fairly straightforward for the baby if that were to happen. I would have been a bit upset about missing the birth but not the end of the world. So I was OK with that as an outcome. I did discuss this with DH because under anaesthetic they don't allow the partner to be there either. He was OK with this too.
I was a bit anxious about it being painful, but I was reassured that I could ask them to stop if if got too much, and it only takes a few minutes, so I felt like I would give it a go. DH apparently immediately looked up a video of it on youtube and then refused to be in the room if I had it done (even though I got them to agree to let him in which they wouldn't have normally allowed because it was during lockdown!). I have not looked up any videos, because I didn't want to have that reaction! I think a lot of things can look a lot more alarming than they are in reality.
In my case even though DS was measuring big, they said they would let me go into labour naturally if the ECV was successful. If it was unsuccessful they would have booked a c-section for approx 39 weeks.
The ECV was booked I think something like 37+6 but I turned up on the day all prepared for a day of monitoring/boredom and they scanned me and he had turned so they told me to go home. They did agree to scan me in early labour to check he was still head down, which he was. He turned out to be extremely long with ridiculous legs - he reminded me of a baby giraffe - but not a big baby, and the labour was totally straightforward.
I have still not looked up the video even though I won't have any more babies. All in all a totally bizarre couple of weeks. Good luck, OP.