I don't use any Google / YouTube or YouTube apps, so I don't know how they behave.

NewPipe it's an open source YouTube client.

From NewPipe on my phone, when I play a video it doesn't force a notification to my laptop.

Instead, with KDE Connect instalked, and with a video playing in NewPipe, if I choose, I can click the music icon in the laptop's taskbar to dee the playback controls.