If my limited knowledge is correct, many braille displays are fairly loud, and you'd hear the clacking when the engineer wasn't typing (if you used a live coding website).

None of the blind engineers I've worked with used them- too slow to refresh, too limited number of characters that can be displayed at once, and/or too expensive. Some are better than others, but they're all expensive.

If I had to guess, the usual tool the engineer used for coding had voiceover support for tab stops, but not in the browser editor.