ZDoom

WMA was not even really supported by FMod, all FMod did was using the Windows ACM to decode unknown files (if it worked, that is)
So Windows has WMA support, but Mac and Linux did not!

The format was never officially supported by ZDoom and no attempts will be made to change that, as there is no decent way to use it. It was ultimately just one more of Microsoft's pathetic proprietary failures. It had a short time to thrive when music downloads were still DRMed.

Wiki page is wrong, WMA is not supported by OpenAL backend. And I don't think it was supported by FMOD on non-Windows platforms.
There are bunch of good free formats, just forget about this one.

doesn't slade 3 uses external plug-ins when dealing with "strange" áudio formats? (like using default Windows plugins to play mp3)

WMA is not exactly an open-source-friendly sound format - I imagine ZDoom support for it was lost when FMod was abandoned, though I can't account for why SLADE might have supported it before.

In one of my maps from 2017 the player encounters an NPC behind a locked gate. The NPC tells the player that s/he must find an alternative path to the destination.

I was playing around in the game today, and met up with the NPC. His message is delivered in text, but not in audio. In the console I used "PlaySound map11vx2", which is properly defined in SNDINFO, and has a sound file in the Sounds/Messages folder. However, the audio message does not play. I looked at the pk3 file in SLADE3, which indicates the sound type is "Unknown". The file is a Windows Media Audio (wma) file, which is [url=https://zdoom.org/wiki/Sound_format]supported by ZDooM[/url]. Therefore, it's puzzling why the sound does not play. I am using GZDooM 3.2.5.

What's even more puzzling is that the sound file was playing fine when I play-tested the game before its release last March. Could the new version of GZDooM have something to do with it? But then, why would SLADE not recognize the wma file format?