You can skip the intro vids by going to \Games\Bethesda.net\Doom Eternal\base\video\boot_sequence and changing the name of ‘Boot_Sequence.bk2’. I just put a ‘Z’ after Sequence.
As for launching Doom Eternal in Steam. If you go to the Bethesda launcher and create a desktop shortcut for Doom Eternal, then right click > Properties on the shortcut. Copy the URL to the clipboard, for example ‘bethesdanet://run/51’. Go to Steam and add the Bethesda launcher (BethesdaNetUpdater.exe) as a non-Steam game. Right click it > Properties > Set Launch Options. Paste the URL in there. Change the title/icon/background/logo of the game. These should do it:
Viola. Unless Steam logs the time you put into non-Steam games then… I don’t really see the point to be honest. I’m glad the game boots straight to the title screen now though. Will try and get Playnite to launch it for logging my time.