It might be helpful if you share a screenshot with example data of what you already have, but here is my solution.
This is the example data I am using:

The Transactions table contains each transaction you make. It can be formatted however you like, but in this example I have simply typed each category by hand (I verified that it also works if you use a pop-up menu) and entered each amount as a currency. If your Category and Amount columns are in different places, you'll have to modify my formula before it can be used.
In the Budget table, I laid out each category in its own column. The "Total" row starts with this formula in Cell B2:
=SUMIF(Transactions::$B,CONCAT("=",B$1),Transactions::$C)
Then using Autofill and putting the formula in the rest of the columns.
I just entered some random numbers as the budget for each category, then formatted them as Currency in Format tool > Cell > Data Format > Currency.
The "Remaining" row uses a simple
=B3-B2
in Cell B4 (use Autofill for the rest) to calculate how much is left in the budget. Negative (or red in my example) means the total exceeds the budget.