Understandable confusion - there's a few things here I can clear up for you. :)

The card back you have in your card back library is correct. That's the one you attained for ranking in Gold, and should be the one displaying / being used in game if you have it applied.

That being said, there is a known bug which is currently being looked into where the incorrect card back is shown during your mulligan phase (it'll always show the lowest card back). Hence if you go second and draw the extra card, you'll see the incorrect card back for that one time.

The release video is a little out of date. Youll notice that it doesn't list Platinum League - it goes Bronze (40+) -> Silver -> Gold -> Diamond. Since that video was released, the ranking system and associated rewards were changed. There's no longer any rank below Bronze 10, and no card back for being in Bronze league. Therefore in that release video, the Bronze 40+ reward is now Silver, the Silver is now what you get for Gold, the Gold is for Platinum, and the two Diamond card backs remain the same.

Ok, that does actually clear some things up.
A little bit disappointing that there is no official source that actually updated this information, neither was there a new uTube video released, nor was there a updated post on the official website. Seems like it is quite hard to find a website with information.

Also, very strange that they did not do the design consistent.
According to you the card back with only the low level leaves green ist the one for gold.
But on the badge and the title the low and middle level are green. Looks like they made last minute changes and did not give a ♥♥♥♥ about changing it everywhere.

I mean, dont get me wrong, I like the game and I understand that it is only a visual thing that does not affect anything else, it just would have been nice if the design of card back, badge and title would have matched.

Anyway, thanks for the info,
keep enjoying the game!

Ben