As a follow up, When did it become common that a person would need to have documentation or other such items, aside from money, on them at all times?

Side note: Consider that there are regional differences in terminology here with terms such as "purse" or "wallet".

For example in American English the word "purse" can mean a handbag whereas in British English it can mean a coin purse and would never refer to a handbag. There are differences also in whether items such as a coin purse are encompassed by the term "wallet" or not.

Why are you making the distinction about it being a bi-fold leather wallet? Shouldn't you just say folding leather wallet? If anything I know more people with tri-fold wallets than bi-fold wallets. That's an interesting follow-up question there too. Which came first, the bi-fold or the tri-fold?

It's not really historical but you may want to ask /r/fashion or /r/malefashionadvice. I know for mfa there are quite a few artisan leather wallet makers who may be able to answer you - a lot of them are interested in the histories of their products, etc.