It's always hard to have to make the decision to rehome a beloved pet. I've had to do it twice before, once with a pair of pet rats and once with a bird. I am still very regretful myself, as you are as well, but if it has taught me anything it is that you shouldn't dwell on the past and to always learn from your mistakes.
I had a pair of rats when I was very young and my mum gave them to a coworker because I barely interacted with them. I was only around 8 or 9 and I didn't fully understand the hard work and commitment of having pets. I didn't clean or change their food often enough and didn't get them out to play everyday. I always regretted not taking responsibility for them and being a good owner, but it taught me a valuable lesson and when I got a rabbit a few years later I was much more mature and responsible in caring for it.
When I first moved to a new state to be with my now ex-boyfriend, I was lonely in a strange new city so I adopted a bird to keep me company. She was a lorikeet and really sweet, I loved her a lot. When I broke up with my ex, I couldn't afford my own place so I had to move into an apartment with two other roommates. They wouldn't let me bring my lorikeet so I had to find a new home for her. It broke my heart and I didn't want to do it but when you are facing being homeless, you have to make hard decisions... It sucked. When I got my own place, I asked the people I gave her to if I could buy her back but they just ignored my calls and emails so I stopped. I still miss her and deeply regret having to rehome her. It was a really hard decision and something I'll have to live with forever but it has gotten easier.
I think rehoming a pet is never a decision to be taken lightly and you should always try to avoid it but sometimes life just doesn't work out the way you want it to... You have to try and move on and just make sure to always learn from your past mistakes so you don't repeat them again. Try not to dwell on it too much and picture them happily in their new homes.
Just to add, with the boyfriend who doesn't like birds, have a chat with him about it. My current BF doesn't love animals as much as me and doesn't understand why I want to have a house filled with them but I calmly spoke to him and told him how pets make me happy and help with my anxiety and depression, I need animals in my life to make me feel at peace. He understands that, and while he doesn't personally want a house filled with birds, he is quite happy to live with them if it makes me happy and it's something that really enriches my life. Maybe have a chat to your BF and tell him how you feel about getting a bird and tell him how important it is to you. Relationships work both ways and it's important to compromise for each other.