Email client with better inbox customization?

Question

Email

Help me find a convenient email client, because Gmail is no longer suitable.
What I need:
- Separate counters, or sections for smart filtering in the following sequence: "unread + work", letters marked "parse later", "other work letters", "other unread letters", "all other letters".
- Collection of mail from three accounts.
- Preferably on the web.
How Gmail does it in its inbox:
- First, the "Parse later" section should go, because if you put it after the working one, then all letters will remain in this category and will not fall into a separate one. Because of this, the unread counter for the first category cannot be configured.
- Unable to do so category "
- I used to use their function from the "Quick Links" lab, it allowed me to save filters and open them in 1 click. Today I found out that for some reason they disable this feature.
In general, Gmail has a backlog for convenient inbox customization, but still everything falls into uncomfortable piles, in an uncomfortable order, and I want to carefully sort everything.