Allays won't pick up any items and give them to the player or noteblocks. Instead, they just fly around with the item in their hand and won't pick up dropped items. This has been an issue in the wild update toggle before 1.19 fully released, it was still an issue in the official release, and still persists in 1.19.2. The screenshot is of two allays I spawned in, gave them both wheat, and threw a bunch of wheat down to see if they'll pick it up. I waited about 1 minute before taking the screenshot to see if they'll pick the wheat up, and they never did.
Do you have the Mob Griefing option turned off? If so, does it work if you turn the option on?