I feel your pain. IMO there is no quick solution for your requirements.
There are a lot of other posts here on this subject that can give you a wealth of useful information about available devices.
But I advise people not to try to sing through their AV system. It's fine for the karaoke music but it's not designed to handle the peaks generated when singing. You could damage your speakers or amplifier.
I recommend a small powered PA to sing through or karaoke microphones.
In your case you might want to consider going the karaoke microphone route to sing through with Youtube playing on your AV system. A lot of the Amazon reviews include videos of people singing to show you what these are capable of.
https://smile.amazon.com/BONAOK-Bluetooth-Microphone-Christmas-Smartphone/dp/B071SGMQ7V
Yes, people use a setup like that.
Some use a very simple setup with the AV system for music and sing with microphones like this.
https://smile.amazon.com/BONAOK-Bluetooth-Microphone-Christmas-Smartphone/dp/B071SGMQ7V
For a minimal system
Karafun
Karaoke Microphones
https://smile.amazon.com/BONAOK-Bluetooth-Microphone-Christmas-Smartphone/dp/B071SGMQ7V
If you want something more substantial there are many posts here about home karaoke systems that contain a wealth of useful information about mics, mixers, and speakers depending on your requirements.