Biden is not responsible for this. It’s the one remaining (of 40) anti-lgbtq “poison-pill” riders on the bill that didn’t get stripped, and it only prohibits “flying” a Pride flag or using State Dept funds from buying new ones. And only until the new budget in September.
What it does not prohibit is draping or festooning Pride flags, painting them on the sides of buildings, rainbow light displays/projections (or any other creative use of pride flags or rainbow/pride displays), nor for existing Pride flags to be used for such purposes or for donated flags, etc. to be used or those supplied privately.
The ban is pretty weak, and almost certainly temporary.