I agree. The way the emails are automatically assigned to a category is not 100% reliable today. If we could add filter to customize it, it will be very useful and avoid manual reassignation.
Maybe categories should just be a selection of folder and/or label that are flagged as such.
I really appreciate the possibility to receive notifications only for certain categories to skip the noise and focus the notifications on the meaningful emails.

While the below comments describe the perfect solution, even just the ability to add a single customisable category would a huge benefit. Being able to customise the category order would also be very helpful.

Categories should function just like folders, but basically they have some preset filters for them. So in that case, we should be able to add any folders to the top as a category. The big one I want is a "finance" one for all banking and credit card related items.

Agreed. To be clearer, I would suggest:
- Being able to rename existing categories
- Being able to create new categories
- Being able to assign custom or preset colours to each
- Being able to define a logic for how emails are captured into these custom categories (maybe even using Lumo)?