I think there is an obvious answer. Canon R5. You said 'prefer full frame'.
Some people have chosen the R3 over the R5. They sacrifice resolution (45mp R5 vs 24mp R3) for the various advantages of the R3.
It is much more expensive and it's heavier.
R3 1,015 g (35.8 oz)
R5 738 g (26.03 oz)
However, as you want to reduce weight, I think that rules out the R3.
R6 is 20mp and R6 MkII is 24mp. I think everyone would agree 45 mp is better for birds than 20 or 24.
R7 is crop. If your full frame preference was negotiable, the R7 should be considered.
If budget is not an issue, R5 and R7 would make a great pair.