Hi Ekosmas. I'm Greg, awarded MVP for eleven years, Volunteer Moderator, and Independent Advisor here to help you until this is resolved.
You said you removed the adapter and disabled in BIOS, but how about disabling in the Device Manager > WIfi Network Adapter > Driver tab > Disable. This should shut off the device. (Uninstall will only reinstall it)
You can also try going into Windows Settings > Network & Internet > Status > Change Adapter Options, right click Wifi to Disable.
Normally having the manufacturer's bloatware in addition WIndows Wifi would not be optimal for performance but it sounds like you don't use it and dont' want the Wifi light on.
Have you tried installing the Sony wifi software in Compatibility Mode:
https://www.groovypost.com/howto/run-old-softwa...
I hope this helps. Based on what you report back I can answer any questions and may have other steps to perform.
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