You have a gorgeous little girl! I saw your other post. Make sure you quarantine her from your other budgie. This means keeping her in her own cage in a separate room for at least a month. I would also wait on introducing her to Gypsy. He needs time to grieve for his friend.
Please be sure to observe quarantine for the new budgie.
Quarantine means housing the new bird in a different cage in a different room than the current bird (as far away from the room the current bird is in as possible) for a period of 35-45 days.
Budgies mask symptoms when they are ill. Symptoms may not show up for over two weeks.
Often you will not even realize your bird is not well. Many budgie illnesses are airborne which is why you need to quarantine your new bird in a completely different room.
It is also a good idea to always take a new budgie in to see an Avian Vet for a "well-birdie" check-up. This allows you to develop a good relationship with the vet and the vet can establish a baseline for your bird in case of any future illnesses or injuries.
They are already talking to each other (we live in an apartment so they can hear each other) and Gypsy has already improved from earlier this week. He's not doing his panicked call for Bar-Bar (which he did all day and night up until last night) and he stopped picking at himself the first time he heard ChiChi chirp. So I'm super happy about that.