How can I bind my Steam game to my Ubisoft account?

I’d like to know if anyone knows how to bind my Steam purchased game to my Ubisoft account. We’re talking about "South Park: The Stick of Truth" in this particular case.

Problem discription:

The thing is that unlike "South Park: The Fractured but Whole", "South Park: The Stick of Truth" doesn’t let you call up the Ubisoft menu (Shift+F2) while in game. In fact it doesn’t even require you to download Ubisoft launcher, thus binding your Steam-purchased copy to your Ubisoft account, even if they are linked.

I also have other games on Steam as well as EpicGames that are Ubisoft’s production (that same mentioned above "South Park: The Fractured but Whole" f.e.), but all of them require Ubisoft launcher and immediately bind with my Ubisoft account upon installation and launch.

Results of my own efforts on the matter:

I’ve tried to search the net and StackExchange for answers, but so far I’ve not found any ways that can work in this case. I’ve also tried contacting Ubisoft support team, but they’ve simply said "NO", without even trying much, I assume.

This said, so far my best guess would be to find a CD key of the said game and use it in Ubisoft launcher in "Activate a key" directory. But neither in the Steam library nor in the Steam receipt I can find it (I’ve checked the options of the game in the library, there is no "CD keys" line, as suggested for other games). Regarding that I have another idea where it might happen to be – the game’s files, but I don’t know exactly where and how to search for it in them.