Comment by dcrazy
This is the job of the Bidi Algorithm: https://www.unicode.org/reports/tr9/
Of course, this is an “annex”, not part of the core Unicode spec. So in situations where you can’t rely on the presentation layer’s (correct) implementation of the Bidi algorithm, you can fall back to directional override/embedding characters.
Over the years I’ve run into a few situations where the rules around neutral characters didn’t produce the right result and so we had to use the override characters to force the correct display. It’s completely a niche but very handy when you are mixing quotes within a complex text.