Moving money to a pot could be considered as either
Deferred spending; if you have a large bill and you’re putting part of it into a pot every month, you are in effect spending that amount on the bill each month, and the actual eventual payment is little more than a finalised settlement of what you’ve already ‘spent’.
Conscious saving; where putting the money into the pot is effectively a statement of “I do not wish to spend this money”. You’ve no real goal for it, but you’re putting the money aside because you don’t want to spend it.
The former is effectively spending. The latter is perhaps effectively committed spending. Either way, the sensible thing would seem to be to take them off the ‘left to spend’ because, either way, the money has been ring-fenced and isn’t actually ‘left to spend’.
I fear at this point Monzo are very muddle about how they are treating pots. In some areas they’re excluding them, in others they aren’t. One could reasonably say that if Monzo are counting money transferred to pots as ‘left to spend’ then they should also count it as full account money, except they aren’t. If you go ‘overdrawn’ in your main account (but your pots more than cover it), you’re considered overdrawn. Pots are excluded just fine there.
There really does need to be some more joined-up thinking, I would say.
I also think the whole setting budgets process could be a lot smarter. An ‘autotune’ button like you get in photo editing apps, except in this case it uses past months to predict your income, and sets your individual budgets according to your past spending pattern and a bit of magic sauce.
Or, simply, once you’ve set an overall budget, it doesn’t let you set any of the individual budgets in such a way you’d go higher than the overall (see for example, Humble Bundle, where if you set the amount you pay and then adjust one tip, it lowers the other tips instead of increasing the amount you pay).