This article may help: https://support.airtable.com/hc/en-us/articles/218734758-A-beginner-s-guide-to-many-to-many-relationships#junction
Make a table for:
The envelope (categories)
The actual expenses
Link the envelop table to expenses. Connect expenses records to the right envelope records. Then “ROLLUP” the expenses and subtract that number from the envelop budget.
Connect the month to envelops. ROLLUP the combined budget for the month and subtract the Rollup of the combined expenses of the month. That’s your monthly surplus or deficit.
Now link the month record to month records. Call that field “previous month”. Use LOOKUP to bring over the deficit or surplus from the previous month
On the income table connect to the month and use LOOKUP again to get the deficit of the corresponding month. Or, make income a field on the month table.
(I typed this on my mobile phone at a weird hour of the day. Pardon typos. Hope this puts you in the right direction)