Thank you again to everyone for your advice!
For future readers looking to answer this question, here is an account of what we did. Please note that I am NOT a vet or any kind of professional when it comes to animals - we just want our birds to live healthy, happy lives, and this was where my best research led me for Passover/Pesach 2020.
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About our birds: I have a 2 yo pet store budgie and a 1 yo breeder conure. Our budgie came to us only eating seeds but she's finally started accepting some fruits and veg (peas, brocc, basil, steamed spinach, sweet potatoes, berries, apples, pears) and pellets, partially due to our daily efforts but largely because she sees our conure eating them. Our conure eats almost any fruit and vegetable we put before her, will occasionally nibble a hard-boiled egg, and loves her pellets.
About our observance: According to our observance of the holiday, we can't have chametz in our home, nor can we benefit from chametz. Our birds are included in this, so for us to maintain their diet we would need to 'sell' them and move them outside of our home.
About 2020: Because of COVID-19, it was not feasible for us to consider 'selling' the birds this year.
What we did, and what happened: I based my menu decisions on previous conversations with our vet (general, not specifically regarding this question), research, and the answers I received on this forum. There are several resources like the one Matto posted (thanks Matto!) indicating which bird food is kitniyot and therefore acceptable as pet food over Passover/Pesach. Unfortunately, to my knowledge they are all seed-only mixes for finches and canaries, and there are no pellet options. I was definitely concerned that our budgie would regress to a seed-only diet and that our conure would develop some bad eating habits.
After comparing the permitted seed mixes, I chose the Finch seed mix because its nutrient breakdown seemed most similar to my budgie's seed mix. I also ordered the HARI supplemental vitamin powder (thanks again, Mizzely!). I prepared baked sweet potato, quinoa, and a carrot-broccoli-cauliflower chop (slightly steamed).
In the mornings, we fed the birds chop along with chopped raw jalapenos and parsley, followed by sweet potato (a big favourite) and quinoa. In the afternoon they were served a small amount of banana mixed with the recommended amount of HARI - neither one of them really cared for it, so it took a lot of patience, hand-feeding, and pressing seeds into the banana, and they still never finished their daily HARI portions. During the day, they ate blueberries, clementine, grapes, apples, and pear as treats, and once had some hard-boiled egg. In the evenings they received more veg and potato, followed by some of the finch seed and millet. I was much more generous in their portions than I normally am because I was concerned they'd be hungrier without the pellets to fill them up, so while I aimed for more nutritious food I did make more food available to them throughout the day.
I did not feed the birds matza or matza products. I am no expert, but I'm very wary of feeding birds real matza: while it is only flour and water, it can be very constipating for humans and I didn't know what effect it would have on them. If anyone has experience/knowledge about this, I'd love to hear about it.
Both birds maintained their weight throughout the holiday, and their behaviour and plumage went unchanged (although difference in the latter is a little hard to note over such a short period of time). Our parakeet's droppings did not change in colour or texture, other than a occasionally having a greater liquid component after eating fruit (which happens normally). Our conure's droppings changed a lot in texture and a little in frequency. She had much, much more liquid and sometimes less solid in her droppings after eating anything other than sweet potato, millet and seeds. She usually has more liquid droppings after fruit, but this was certainly more than the usual amount, sometimes almost entirely clear liquid. Looking back and based on what I've read, I would attribute this to the greater water content in the steamed chop, which I froze in batches to defrost before serving (and which she had throughout the day), and to the quinoa, which is not usually as significant a part of her diet.
We resumed the birds' normal diet after the holiday and our conure's droppings immediately returned to their normal appearance.
Future plans: I am very aware of the risks attached to such a significant change in diet, and I was very very anxious throughout this experience, pretty much until I saw our conure's system return to normal. I definitely intend to speak with the vet about this particular question at our next appointment, so that I can be more informed if such a situation were to arise again (and I will definitely try to update this post with the results of that conversation). Otherwise, provided that COVID is under control by Passover/Pesach 2021, we will probably aim to 'sell' our birds next year so they can maintain their normal pelleted diet.