I spent a lot of time and managed to make errors in vs code more visible. Still not in the gutter, but better then nothing. I replaced vs code squiggly error and warning underlines with background and thick underline:


(offtop: also on screenshot you can see how "Bracket Pair Colorizer" extension works :)
Install CSS and JS Loader and carefully follow all instructions (i had problem with link to css, which in windows must be like file:///C:/myfolder/myfile.css ... better read whole extension instructions)
Create a css file with contents:
.monaco-editor.vs .squiggly-warning,
.monaco-editor.vs-dark .squiggly-warning {
/* background */
background: #f2e3b3;
/* underline */
border-bottom: 3px solid #ffc000;
}
.monaco-editor.vs .squiggly-error,
.monaco-editor.vs-dark .squiggly-error {
/* background */
background: #ffc7c7;
/* underline */
border-bottom: 4px solid #ff0000;
}
And place link to it in settings.json like said in CSS and JS Loader extension instructions
"vscode_custom_css.imports": ["file:///C:/yourfolder/youfilewithcustom.css"],
"vscode_custom_css.policy": true,
, then reload...
You can get color box around error (instead of underline, not simultaniously) if you use for example (border: instead of border-bottom: ):
border: 1px solid #ff0000;
Or you can get custom border from any side (right border alone seems to look great, tried this while writing this post)

.monaco-editor.vs .squiggly-warning,
.monaco-editor.vs-dark .squiggly-warning {
background: #f2e3b3;
border-right: 5px solid #ffc000;
border-bottom: 5px solid #ffc000;
border-top: 3px solid #ffc000;
border-left: 1px solid #ffc000;
}
.monaco-editor.vs .squiggly-error,
.monaco-editor.vs-dark .squiggly-error {
background: #ffc7c7;
border-right: 5px solid #ff0000;
border-bottom: 3px solid #ff0000;
border-top: 3px solid #ff0000;
border-left: 1px solid #ff0000;
}
This css will only replace squiggle color from green to yellow:
.monaco-editor.vs .squiggly-warning,
.monaco-editor.vs-dark .squiggly-warning {
/* yellow squiggly */
background: url("data:image/svg+xml;charset=utf-8,<svg xmlns='http://www.w3.org/2000/svg' height='3' width='6'><g fill='#FF0'><path d='M5.5 0l-3 3H1.1l3-3z'/><path d='M4 0l2 2V.6L5.4 0zM0 2l1 1h1.4L0 .6z'/></g></svg>") repeat-x 0 100%;
}
As you can see the name of class changed from .greensquiggly to .squiggly-warning, that's why css from previous answer doesn't work.
To find out new error css class i used Help -> Toggle Developer Tools, where after deleting bunch of blocks, i could find the error and warning classes.