In Stable Build v1.63 there is a new method for highlighting various Unicode characters that might otherwise be difficult to spot in your code. These are the new settings:

You can use these colorCustomizations
to change the default orange borders:
{
"workbench.colorCustomizations": {
"editorUnicodeHighlight.border": "#00ff37",
"editorUnicodeHighlight.background": "#f00", // will be in vscode v1.66
// "minimap.unicodeHighlight": "#ff0000", // removed in v1.64
// "editorOverviewRuler.unicodeForeground": "#ff0000" // removed in v1.64
}
Apparently, indicators for these Unicode warnings will not be shown in the minimap or overview ruler as of v1.64, see Consider removing the Unicode highlight scroll bar decoration
Here is how a Unicode zero-width space (U+200B) appears with these settings:

The zero-width character is an invisible Unicode character controlled by the Unicode Highlight: Invisible Characters
setting above.
From v1.63 release notes: Unicode highlighting
Read this article or this article for how invisible or confusable
Unicode characters can be used in Unicode spoofing attacks.
Note that this feature does not detect all possible Unicode spoofing
attacks, as this depends on your font and locale settings. Also, the
detection of ambiguous characters is done heuristically. To be on the
safe side, the restricted mode of the workspace trust should be used
to review source code, as all non-ASCII characters are highlighted in
untrusted workspaces.
The settings editor.unicodeHighlight.invisibleCharacters
,
editor.unicodeHighlight.ambiguousCharacters
or
editor.unicodeHighlight.nonBasicASCII
can be set to false to disable
the corresponding feature.
Individual characters can be excluded from being highlighted and
characters in comments or text and markdown documents are not
highlighted by default.