I fully agree with you about debt/credit. If I give you something without getting anything in return, that can be considered debt.
The point I'm specifically trying to come to grips with is the idea that money came before barter: considering that money is used as a token that is itself bartered for goods or services, I can't understand how money came before barter. It just doesn't make sense, using money is barter.
The idea isn’t that money came before barter - barter has always been around on the fringes of things. It’s that credit came before money & that credit tokens backed by a credible issuer turned out to be extremely useful as tokens of exchange & units of account. Hence it’s credit that evolves into money, not the things you might have bartered occasionally. Barter was for exchange with people you didn’t trust & didn’t have any kind of on-going relationship with & was therefore rare & fairly irrelevant economically. Anyone worth doing business with had some kind of credit relationship with your state anyway.
I'll answer your question: barter came after money because the barter systems that emerged came after money and they marked to a currency to measure the barter transaction. IOW, they used a virtual currency. Even Charlemagne's empire defined a virtual currency that was used hundreds of years after the empire fell apart and Charlemagne never even ever struck coin but only left behind a specification of the HRE currency.
The point I'm specifically trying to come to grips with is the idea that money came before barter: considering that money is used as a token that is itself bartered for goods or services, I can't understand how money came before barter. It just doesn't make sense, using money is barter.