Here goes what I think-
Well, I think while Dumbledore and Harry were facing Draco and others here, Fawkes was somewhere watching over someone on Dumby's orders so that they could get some info about the Horcruxes which could be revealed in the final book.
Maybe b'coz Dumby knew that he's going to die( Or fake his death), he didnt need fawkes over here or if he's really dead he might have wanted Fawkes to help Harry out with the Horcruxes while he's not around and so Fawkes was somewhere else.
Fawkes' tears have an amazing healing power so maybe he'll help Harry survive in his final battle against Voldemort. Also Harry and Lord V's wands have Fawkes feather. Being related, the wands shouldnot be used against each other but if used that way, maybe the fact that Fawkes is on Harry's side wilh have some significance in turning things to favour Harry's position in the final battle,
We can only guess though 😊
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