My budgie is extremely territorial

[peesh]

I took my budgie, Rayfa, home when she was around 3 months old back in September 2021. Ever since she's been pretty aggressive and territorial, much more so than my older female, Peeko. Peeko probably saw her as a baby, so back then they would preen and feed each other. Then, Rayfa became very demanding of Peeko and would chase her asking to be fed. At around 5 months she had a tendency (while not being hand tame) to come onto my hand and bite me hard once and then come back onto her perch. I didn't react and took it as her protecting her territory, and thought it was fair. After a couple weeks of that she stopped, so I assumed it was her teenage phase. Back then we (my birds and I) lived in a big room with another person where both Peeko and Rei went outside together and got along okay-ish. Peeko herself is very timid and doesn't like fighting / chewing toys / biting me etc. so when she feels uncomfortable with Rayfa she just goes higher up away from her. Rayfa, on the other hand, always goes straight to biting and squawking when things don't go her way. Now, we moved to a smaller room where it's just me and my birds. They've started getting 3-4 hours outside instead of the previous 1-2. Recently I converted them to a seed mix where there is less millet, so they've become much more tame knowing I can give them the tasty stuff. They've also been more interested in exploring the room, finding millet seeds they've dropped and looking into shelves and such. Still, Rayfa is very territorial in every aspect of it. When roaming the room, she would always squawk at Peeko to be farther away from her. She comes to my hands easily and doesn't want Peeko on them either. Sometimes she comes onto my hands and stretches her neck out to be closer to my face, and when I do being it closer, she would nibble my nose (not quite bite, but still a bit painful). She would also come onto my hands and bite my fingers very hard if there are no treats, but still stay on them after biting. I never ever react to her bites in any way, but she keeps doing that. I never come close to her if she shows that she doesn't want me near her. The final straw was when I was giving treats to Peeko and Rayfa kept coming onto my hand, and I had to put her back several times before I couldn't anymore. After that, she came onto my hand, then onto my shoulder, then closer to my face and bit my nose very hard (probably as hard as she could).
Now, I don't understand what in particular causes her constant biting. Is it her territorial personality, or is she jealous of Peeko when I give her attention and treats too? Is it both? And how can I make this biting and squawking happen less?

 

[peesh]

Adding onto this, she's been enjoying sitting on my shoulder and head recently. I'm starting to think she really is just jealous of Peeko and dislikes her because of that.