Looking to create a website similar to YNAB the concept is you get paid a certain amount and it can be different each week and month. With your paycheck you will create a budget what your money needs to do before your next paycheck. You will create a budget based on what you get paid and budget that money and track expenses. You will have the ability for different categories on the website. To be able to see your debt being paid off how long it will take to get paid off and different plans of paying it off. Bills set up when they are dew and a reminder to not be late and be able to pay them on time. Savings goals.
If you are talking about the site actually handling the funds and actively saving/dispensing etc actual money then you need to adhere to banking regulations, compliance etc. You can’t just apply for this - it’s very complicated and very expensive
Even minus that functionality you are not going to find close to this on a stock website - it would require VERY expensive custom development let alone the hosting and security requirements.
Not talking about a bank but software that will help people budget.
Probably your best option would be to search for budget tracker plugins and try to integrate one of these with a theme as you won’t find that even without the find management as an out of the box solution.
Either way I would expect it to require some fairly heavy weight customisation.
There are numerous apps, software etc that does this - could you use one of those?
These other sites etc (that do this properly) would be tens of thousands of $ to recreate