I've got new update Blender 3.0 and new driver 21.Q4, my VGA AMD RX590 is not displayed in the section Cycles Render - HIP.
I removed all Blender files and card drivers then installed it again, but nothing. It can be seen in the screenshots
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You GPU doesn't meet the minimum requirements. Please always consult the manual for up to date system requirements.
In the message dialog it states
Requires discrete AMD GPU with RDNA architecture
On the Wikipedia page for RX500 series AMD GPUs you can read on the very first line
These cards are based on the fourth iteration of the Graphics Core Next architecture
Graphics Core Next architecture is a predecessor of newer RDNA, which was first introduced with the Radeon RX 5000 series of video cards, launched on July 7, 2019.
If your card is older than this date, or has a model number of the series RX500, RX400, RX300, RX200, HD8000, HD700, or earlier it is not supported by the HIP API at the moment of writing (early 2022).