Monzo does have IFTTT integration (which in turn works with Stringify, which can enable you to chain actions and triggers iirc). I remember seeing on the “Monzo & IFTTT - Share your creations here!” thread that someone did magic with spreadsheets to make a dynamic daily budget. If it’s possible to use spreadsheets to make a widget display a set proportion of available funds, you might be able to get it to calculate a percentage of all incoming payments.
No idea how you would implement this, but it could be possible; though you can’t use IFTTT to automate transfers to another bank, only to a pot (which is almost like a linked savings account in terms of how it looks, but it’s not a separate account with its own number.) This can reduce hassle in terms of logging into different bank sites/apps to see where you’re up to, as it would all be within the one app. You can’t spend the money in pots by accident, it’s kept separate from your “active balance,” so to speak.