Earlier quoted context omitted.
Which dictionary are you using that doesn’t mark it as an archaic form in British English?
Merriam-Webster has it as "chiefly British spelling" of jail, and Oxford English Dictionary has it as a "variant". https://www.merriam-webster.com/dictionary/gaol https://www.oed.com/search/dictionary/?q=gaol
https://www.collinsdictionary.com/dictionary/english/gaol
I believe Collins is the standard dictionary that British people use, much like Merriam-Webster for Americans.