You'll need a paid version of the YouTube app it you want it to carry on playing in the background. There are currently free trials available (as a bloody annoying pop-up advert reminds me every time I try to use it!)
I feel this needs a bit more emphasis.
"Youtube video soundtracks in one browser tab and then open a new tab"
Your Android has a multi tasking OS - it's Linux. The Youtube limitation you mention is MARKETING. Google have chosen that you must pay to get that facility.
Much material on YT is also on other "podcast" platforms. After trying a few I use the Apple one via a browser. Still many annoyances but no login required, auto plays (but ONLY newest first - grrrrrrrr).