I have a similar problem - with the difference that I use Duolingo as a PWA (in Vanadium) in a profile without GSF, Play services and Play Store. Everything works fine except for the voice input.
I have enabled the microphone for Duolingo in Vanadium >Site settings and also in Privacy>Permission manager>Microphone.
The Settings>System>Languages>Voice Input page is empty for me, it looks like I can't install anything here.
Is it necessary to install Google Speech recognition and if so can I install it in the owner profile and then install and use it in the un-Googled profile via Manage users>install available apps?
Or is there perhaps a FOSS alternative? I have read about Sayboard and Dicio in other forums - does anyone have experience with them?