I don't really get why Picard tear of that "Romulans Only" sign and then went into the bar. For once it is really stupid as he must know it would provoke the present Romulans. But even more so it doesn't make really sense considering what went on before. I mean he saw how poor that place it and voiced regrets to the nuns and Elnor for abandoning them completely. The last episodes made clear that he thought that the Federation and Starfleet acted completely wrong in abandoning the rescue efforts and in this episode he admitted even before the bar incident his part in it all, that he should have tried more.
So why go the provocation route? He must understand why Romulans are not a fan of humans and other Federation members right now. And especially why they wouldn't like him personally after he broke his promises. So why not try to make amends and get rid of that "Romulans Only" sign with that speech he hold after the sword fight? Something to build some bridges and lessen the hurt. Instead he just acted so much like he deserved respect from those Romulans around him and then threw a hissy fit when they didn't give it to him. That felt off after he already admitted to the nuns and Elnor that his past actions and especially the actions of the Federation and Starfleet were wrong.
actually, i consider that scene quite important, it's the moment when his mode changes from there is something i should do to ... and damn the torpedos