Nope. Mutual credit system is not about group share expenses…
is about avoid national currency within local community (you may have no money, but still you have skills to offer),
and is about support local businesses (because you may spend your earned “credit units” only within community),
and in some cases is about to avoid risks of inflation of national currency (mutual credit is “money”, which supply is equal to what community actually have to offer, it issues while people serve each other and erases while credit clearing process.
I tried to find out some app providing mutual credit system or timebank, but I only found some online local services. And in the case of app or bot this system may be implemented just anywhere.
It is indeed different in goals, but is the same in usage: people start with the same amount of units and exchange it. A sharing expense app can be used for that.
There is a difference in the scope of users: in your description I understood that everyone would be part of a single chat group, in which case a webxdc app works. But if the community is bigger it might get unwieldy to have everyone in the same group chat, so a bot that anyone can talk to 1-to-1 becomes handy.