How to preserve session in Safari private window mode? I'm comparatively new to Mac OS.

I was a Chrome user before. In Incognito mode, it preserves the session, i.e., if you have logged in to Google and you open YouTube in the same window (but in a new tab), it automatically signs me in for that particular Gmail user in YouTube, whereas in Safari private window mode, I have to login everytime I open something new in a new tab.

I was wondering if I could make it just like Chrome by changing a few settings.
If you prefer the way that Chrome works, I would suggest using Chrome on OS X. In Incognito mode, it works the way you want.