GlobalNavButtons uses Mustache to preprocess your global configuration, which its syntax is very similar to wikitext. Unfortunately, that includes its sanitization rules, so you can't inject an image tag in there.

You'll need to fork/modify the script and include support for an image or icon parameter, whether it's from user input or from Fandom's global-explore-navigation__icon, starting from here:

https://dev.fandom.com/wiki/MediaWiki:GlobalNavButtons.js#L-77

Edit: I utterly misread your post, apologies. I'll need to create a new one below

With how the script injects icons, it must be something that global-explore-navigation__icon accepts. I do not know how the icon part is handled after the Mustache expansion and appending to the DOM, you'll need to ask the script's maintainer(s), or wait a bit until someone else responds to this

^ Ok, thank you for letting me know!

The thing doesnt really parse anything lol, it just plops whatever you give it into the icon socket, your link shows you wanna use icons that are svgs, so just copy the svg html and paste that in the icon argument as a plain string, and if you wanna use an image then just add an <img> tag as input instead, for example an image:

{
text: 'Me',
url: mw.util.getUrl('User:PopularAbbyeet'),
isMain: true,
whoIsMain: false,
shortName: 'Me',
icon: '<img src="https://static.wikia.nocookie.net/dev/images/4/4a/Site-favicon.ico/revision/latest?cb=20210803184000" height="24" width="24" />',
},

And an example of an svg:

{
text: 'Me',
url: mw.util.getUrl('User:PopularAbbyeet'),
isMain: true,
whoIsMain: false,
shortName: 'Me',
icon: '<svg id="wds-icons-discussions" viewBox="0 0 24 24" width="24px" height="24px"><path d="M16,17c0,0.55-0.45,1-1,1H7.41l-5.71,5.71C1.52,23.9,1.26,24,1,24c-0.13,0-0.26-0.02-0.38-0.08C0.24,23.77,0,23.4,0,23V7	c0-0.55,0.45-1,1-1s1,0.45,1,1v13.59l4.29-4.29C6.48,16.11,6.73,16,7,16h8C15.55,16,16,16.45,16,17z M24,4v14	c0,0.4-0.24,0.77-0.62,0.92C23.26,18.98,23.13,19,23,19c-0.26,0-0.52-0.1-0.71-0.29L16.59,13H9c-2.21,0-4-1.79-4-4V4	c0-2.21,1.79-4,4-4h11C22.21,0,24,1.79,24,4z M22,4c0-1.1-0.9-2-2-2H9C7.9,2,7,2.9,7,4v5c0,1.1,0.9,2,2,2h8	c0.27,0,0.52,0.11,0.71,0.29L22,15.59V4z"></path></svg>',
},

^ thank you so much!

How do you find the SVG data of the icons? Sorry, I've never dealt with that file type

SVG files are XML-formatted, so they're able to be opened in Devtools or a text/code editor

^ Ok, thank you!!