So I tried this, but for me actually it does not seem fixed. Before with the bright black theme, the logo was gog.com but not in one long word (rectangular logo), but instead it was a square logo with gog in the first line and com in the second line.
Now it is one long word, which messes up the whole navigation bar since everything else after it is moved to the right.

Anyone else seeing this?

I see exactly what you describe, but I don't know what was before, since I have always used Classic 2014 (square logo, grey background).

Basically both 'Bright black' and 'GOG Classic 2012' themes were using the same logo endpoint, which was removed from GOG servers at some point (you can see it from the script's changelog). So if you mean the black-and-white square logo, then it's the current logo GOG uses, and you were probably using it, since the themes became broken for the reason above.

Not sure about the messing navigation bar part, can you provide a screenshot of it?

I mean the logo from "Bright black", which I realized was removed. But your replacement (not sure where you got it), is not the same. The one now is rectangular. But the old one was also square.

See the screenshot of the navigation bar for how it looks with the black and white logo and the "new" colourful one.
I also attached how the old logo looked.

There were two variants of the old logo. You probably want Classic 2014.

Well I admit I'm not 100% sure how the old logo looked, but I definitely had not Classic 2014, that has a grey navigation bar. I had the bright black, but before gog removed the old logo (however it actually looked like), that one was working fine and not breaking the navigation bar.

My replacement should be the same, as it was taken from archive.org to fill the removed part, previously provided by GOG.
And per my understanding, the square colorful logo (the 2014 classic one) never was an official logo, but rather a creative invention by Barefoot_Monkey, the original author of this script, of combining the color of rectangular 2012 one with the square form of 2014 one, so this variant can be only seen as part of the 2014 classic theme (since 2012 the official GOG logos are the rectangular colorful one and the square black-and-white one, not sure if there were any more pre 2012).
Also 'Bright black' theme is basically a dark theme variation of the 'Classic 2012' one, both using the same rectangular logo.

As per your navigation screenshot, you have either a too small monitor to fill all this bar or too much zoom-in.
I can recommend next actions:
- use 'Default without the stripe' theme;
- remove friends/wishlist icons, as they are redundant and can be found through the account dropdown;
- zoom back to make elements taking less space;

Well... look I don't want to complain, since I'm grateful you are maintaining this script.
But I have a 4k monitor, it is not too small. My browser zoom is 100% like always. (See my newly attached screenshot, were I did not crop the long black extra stuff...). And even when I change zoom, it changes exactly nothing. It is still broken.
I have made zero changes to any settings on my computer. And I have always been using the bright black theme. And before the logo was removed it was working without any issues.

I don't know why, but the replacement from archive.org breaks the whole navigation bar.
(If you say you can not fix it, no problem, I'll adapt to something different. I just liked the colourful logo and was happy that you said it is fixed.)