Does your bank not offer this as a basic service? I think most banks do.

You can assign incoming and outgoing transactions into folders and do stuff like assign repeating transactions automatically to a folder and set targets. So you can make a folder "Saving for a new car" and occasionally add some money to that. Or create a folder "Rent money" and make sure it's topped off and rent payments always go out of that folder. You can setup so a part of your wage automatically gets assigned to that folder for example, so you can easily see how much you have left after assigning money to stuff like rent/mortgage and a food budget for example.

I thought all banks offered this, but it might be different in other countries, or perhaps a paid service?

But even if the bank doesn't offer this, people used to do this in spreadsheet software or dedicated software for years. And even before that, a lot of people used to do this kind of stuff in a little book. In a lot of languages there is even a name for this called Haushaltsbuch in German and Kakeibo in English (from Japanese). I used to do it in Lotus 1-2-3 back in the 80s, later in the 90s I think I had Microsoft Money which worked pretty good, but a spreadsheet was more flexible.

So nobody is stopping you, you can just do this.