Have you checked if there is a Hardware switch for the BT / WIFI , my HP has it via Fn + f2 so effectively a keyboard ON/OFF switch , a clue is the message saying that you need to enable it even though it shows in Device Manager. Have a good look at upper keyboard icons and see if you see one similar to a wireless or BT icon. Win 10 might also have an ON/OFF button for BT as well as WIFI in Quick menu bottom rhs of screen .
Another game I have seen on an older HP was BT was disabled on Win 7 ( but WIFI was On ) then after upgrade to a fresh install of Win 10 it would not show or allow turning ON BT , WIFI was fine , I had to go back to Win 7 , ENABLE the BT and revert to Win 10 again ( Luckily it was a dual boot ) I have seen it done by removing WIFI card fitting to another same model PC and turn ON then swap back.
HP wireless assistant from Win 7 can also cause issues if it was set to DISABLE BT before an upgrade / fresh install , Wireless Assistant is not available in Win 10.
I think there is a hardware switch ( or a switchable USB port ) on the BT /WIFI card that once flipped can be hard to unflip via a new OS , not that this is definitely your case as you may not have upgraded to Win 10 but thought I'd make you aware of the issues that can arise.
You could try UNINSTALLING BT and WIFI via Device Manager and tell Win 10 to remove drivers , turn off PC , swap PCI card to another slot and reboot , it may awaken card ? If it does then swap it back if it is in close proximity to other hardware , or just leave it .
Have you tried this driver from HP looks like there were issues with old realtek wifi/BT driver it says from April 2020 in this document and it lists your model range :
https://support.hp.com/gb-en/document/c06624305
I also found this when using Google searching for 1.7.1021.3000 driver as suggested in the above document on HP help forum :
1.7.1021.3000 Dec 6, 2019
https://ftp.hp.com/pub/softpaq/sp100501-101000/sp100556.exe
Fix and enhancements:
- Fixes an issue where a Bluetooth mouse paired to the system does not function properly after the Bluetooth speaker/headset is changed to the HFP profile.
- Fixes an issue on a system connected to a Bluetooth mouse which causes an error symbol (yellow bang) to be displayed after the system is idle for a period of time.
- Enhances WLAN/Bluetooth coexistence
The Softpaq from HP above MAY act differently to just a driver pack from MS below, it might be worth unpacking it and having a look , firing the .exe file above will unpack it to the front of C: drive usually to an HP folder with loads of other sp files from HP.
or from Microsoft catalogue , there are a few here , it has 1.7.1021.3000 and it also goes up to 1.8.1027.3000 , however the newer versions may not support your VID / PID on the BT part of the card , but will cause no harm if they do not work , but
DO MAKE a SYSTEM RESTORE point before trying drivers above 1.7.1021.3000 as thats as high as HP recommend .
https://www.catalog.update.microsoft.com/Search.aspx?q=VID_0BDA&PID_B001
Good Luck .