How and when would we prune this?

We have this beautiful established bougainvillea growing over a pergola in the backyard of our new home. It’s all growing in pots. We absolutely love it but it’s quite woody and not flowering much (though is very green). It’s also looking a bit too wild and like it could do with a bit of a reshape? Maybe? Never had to consider tackling something so big and don’t want to kill it.

It also looks like some of the new growth is dying…. Not sure what this is about. Do we need to repot into bigger pots maybe?

Any help / suggestions of how to keep this alive and when to prune and how much to cut back would be appreciated.