If you are looking for a system that works inside of Notes, that's a tall order. There's a guy on YouTube (New Perspectives) who made a shortcut that sort of does this. If memory serves it tracks only round numbers, no cents, to give you an at-a-glance idea of what you're spending. Coincidentally, I downloaded and deleted his shortcut a couple days ago.
Personally I think this is asking too much of Notes. You're better off using a spreadsheet or a purpose-built app for running totals and calculations. Having said this, I record all my expenses in Notes (I have 35 years of data backed up to one big text file). I record the data in consistently defined columns (Date, Category, Amount, Vendor) so I can select the text, copy it, and paste into a spreadsheet or load into a money tracking app. I don't do a lot of calculation, I search the data for answers such as where, when, how much did I pay for something. For fun I loaded all the Apple entries into a spreadsheet - shockingly large amount, I was depressed for weeks!