Connect the device you are listening to YouTube on to your ADI 2. Without knowing which device you are using, it's difficult to give more concrete information.

I watch YouTube  on a desktop PC which is connected to my RME device via USB. My studio monitors and headphones are also connected to the RME. It's as easy as setting the Source to USB, pressing play, and adjusting the volume.

A lot to unpack here, if you're using your rme dac for media consumption and you don't need asio or dsd I'll recommend putting the dac into UAC2 mode, (In Device Manager select the ADI-2 DAC under Sound, Video
and Game Controllers, right click and choose Uninstall. In the next dialog make sure to check
'Delete the driver software for this device' confirm, and restart your machine.), you'll know if the dac is in uac2 mode if the rme icon isn't present in notification area. next right click on speaker icon and select "sounds", click on playback tab, right click on rme and enable both "set as default device" and "set as default communication device" and hit apply but don't close the dialog box yet, right click on the rme again and select properties, click on spatial sound tab and make sure it's turned off, next click on advanced, under default format set it to 32bit 48000hz, and enable everything in exclusive mode section, next go to levels tab and set it to 100% for the best quality.
To get the most out of your dac set filter to either sharp or slow, sharp will work better in most cases, (slow can fix resonant ringing issues with some speakers and headphones that have metal drivers (like Focal Elear etc...))
Next set up bit perfect playback via WASAPI, you'll need a player that supports it, MPC BE is a good choice for audio and video playback, open options box and go to audio, under audio section set default renderer to "0. mpc audio renderer" click to properties, under the sound device select RME, set wasapi mode to exclusive, set wasapi method to event, set buffer to default, and enable the following settings -allow bit exact output -use system layout -alternative check for supported format -release device when idle. turn everything else off. next go to sound processing and enable "down mix to" and select "stereo", enable int 16, 24, and 32. Disable everything else.
I recommend checking if your chain is operating in bit perfect mode (manual section 31.14, page 67)

Don't bother - the compression is too high.

Use other services and do your DAC justice.

Latest YT audio streaming with Opus 251 codec (i.e. nearly all new YT vids of the last few years, check 'Stats For Nerds') can sound incredibly good, nothing shameful about using a great DAC to hear it even better!

Thank you, everything works fine

It's the best perceptual encoder we have right now, so I beg to differ, it can sound really good. I say this as someone mastering tracks at 24/96 all day every day on ATCs. Is it as good? No. Can it sound great? Yes, IMO. Check some of these:

https://www.youtube.com/@onemic-theminimalist/videos

I have a very mixed picture on the Youtube sound.

My best guess is, it largely depends on the quality people do when recording and upload stuff, not too much on what happens inside YouTube.

There are artist that recorded at my studio, when I hear the result on YouTube I have nothing to complain about.

I have an ADI-2 PRO AE, ADI-2 DAC, and ADI-2 Pro FSR. However, when I run YouTube, I am stressed because of the severe screen and voice disconnection. I also have Chord Electronics Hugo2, which doesn't happen in Hugo. Can't you improve this phenomenon?

I am replying to your inquiry.

Q1: Was the audio lagging or was it in front of the picture?
A1: Video is affected simultaneously when audio is disconnected.

Q2: Are you playing YouTube on your PC?
A2: Yes, I'm using Windows 11 OS Desktop & Laptop.
Note that some PCs do not experience this problem, but the difference is the Visual C++ service pack. There may be conflicts with other software using RME Driver and C++.
Please refer to the problem improvement.

Q3: ADI-2 connected via USB?
A3: Yes