That could be done with a few influential terminal emulators adopting a consensus extension to ISO8613-6, like this: ESC[38:99:‹purpose›m for foreground, ESC[48:99:‹purpose›m for background.

e.g.

    Foreground     Background    Purpose
    -----------    -----------   -------
    ESC[38:99:0m    ESC[48:99:0m   normal ( same as ESC[39m and ESC[49m )
    ESC[38:99:1m    ESC[48:99:1m   emphasise
    ESC[38:99:2m    ESC[48:99:2m   de-emphasise
    ESC[38:99:3m    ESC[48:99:3m   error
    ESC[38:99:4m    ESC[48:99:4m   warning
    ESC[38:99:5m    ESC[48:99:5m   caution
    ESC[38:99:6m    ESC[48:99:6m   notice

Then people (themes) could easily choose foreground colour or background highlighting for particular roles. Some terminal emulators might also choose to configure other stylistic choices like bold, italic, etc.

(I believe ISO8613-6 defines sub-modes 0 through 5 (te;db), with 2 (rgb) and 5 (256-color indexed) being most widely implemented. But some terminals historically mess up : and ; in CSI sequences, and I know at least one would interpret ESC[38:6:1m as ESC[6;1m (blinking bold!), so here I pick 99 (ECMA-48 defines modes up to 65).)