Container bougieÂs will stunt when in too small a pot & seem to do better in a deep pot. I bought a gallon size plant, replanted it into a 5 gallon container & now it is in a 25 gallon container. It is really taking off in the deep container.
Mine seemed to suffer with transplantation. I would wait until it has recovered from transplantation before pruning it.

They don't like to have their roots disturbed, so make sure to be gentle with the roots if you transplant it. This might be hard, since your plant is so large but in such a small pot it may be severely rootbound, in which case you'll have to disturb the roots, so you may expect to see it suffer a bit in the process. Generally you should only go up one size at a time when you repot a plant, but even going to a 6" pot it's still going to be too small for that plant, so I think you can break the rules in this case and go up a couple sizes.

I would wait until spring to repot it, unless you are supplementing lighting since we are going into winter. They can be grown as Bonsai and being in the too small pot won't hurt it.

I would cut the pot, when you do repot, to disturb the roots as little as possible.

All the above sound good advice, any move sets them back. I'd go for a much bigger pot but well drained mix.

I recently received cuttings from a triple petal blossom bouganvilla
and wonder if it is possibe to root them. I would love your advice. They are in
water and were cut 48 hours ago.