How can I cheer up my wife with BPD and anxiety?

Needs to talk to a doctor about it or even counseling (a lot of counsellors do zoom appointments)

As @Al_Phoenix suggested, stop trying to get her to go out. When I refuse to leave the house, it’s usually a lovely cocktail of confidence issues, self-loathing and hopelessness. Every so often, my flatmate and I will have a “Hoe Day” which sounds ridiculous at first, but essentially dolling yourself up as if you’re going out and then just staying in the flat. Maybe you and your wife could dress up all swanky and have a romantic evening inside? I’m thinking cook a romantic meal or get her favourite carry out but serve it with the table set very professionally. Don’t spring it on her, tell her you’re planning it and set aside a time. This will let her the chance to seek pleasure in making herself feel special and beautiful. A relaxing bath, legs shaved, hair and make up done etc. I’m a big tomboy but I still like to feel special. This can be in whatever way she usually flourishes. If she feels good about herself and has an event to look forward to inside, it may be a step forward for her current low moods and break up her routine a bit. This may be a long shot, but it can serve many purposes. It provides a setting to focus on both of you, that will both boost her within her own space and allow you the chance to spend quality time with your wife.

Showing her you're paying attention to even the little things she needs goes such a long way

I know after i got out of the psych hospital i was stuck inside all the time with horrible fear and depression. I'd try to stop getting her to go out and instead try to help her find some activities that you two can do together inside- a calm video game (not online at first), board game, or even just cuddle to a movie. Pay attention to those little tiny things- give her something in her favorite color, or from her favorite TV show...did she mention needing a new hairbrush? Surprise her with one. Those little things help so much and just build up from there