In reply to:

in British it is considered to be a formal form of while..


I never thought of it as formal form of while-- just a word use in UK that is not use in US (and unsure about rest of world. )

I worked for Xerox, and our documentation for equipment was written in UK-- it would have lines like
"Whilst holding the nut with a spanner..."
These caused problems, since about 50% of tech's where not native speaker of English-- we had the usual poliglot of nationalities, and languages-- including one (native) Farsi speaker.

Having the word spanner-- not wrench in the sentance-- with whilst-- was just too much!