My email goes through K9 on Android first (5.6, the next version broke this workflow and despised about half of its users. Look for k9 overview screen to appreciate the drama and look at the distribution of the stars of the app.) I use K9 to look at the titles of the messages I get on my POP3 accounts. I don't remove the messages from the servers. I disable notifications and polling. I have to manually check my accounts. This is not to be distracted.
Really urgent matters ring my phone. Customers reach me on slack (only on desktop.) IMs are for real time communication. Email is for low priority communication. I check it a few times per day, less than five. I read immediately the important messages and I reply from there, automatically BCC to me. I delete the cruft (the notifications I don't have to archive, invites to events I won't go to, etc.) For many messages the title is the only important signal.
Later on, not every day, I download mail on my laptop with Thunderbird. This deletes email from the POP3 servers so it makes it unavailable to the phone. Messages are organized into a few hundred of folders, either by sender or project. Filters do it (create it once, use forever.)
This means that I already read the email, at least its title, and I rarely have to read it again on the computer. I got thousands of unread messages there and I have read only the title of many of them, only on the phone. I've got messages dating back to 1994.
Of course I'm an outlier (but consider how many people want the old K9 back) and of course predicting how people use stuff is very hard. It would be nice to have an IMAP server over my Thunderbird folder to look at every message from my phone. It's been 10 years since I told me that maybe I should self host one and I never did it, so it's probably not very important though.
I have a few broad search filters (example, at work: internal email vs outside email.) I star or bookmark things I need to come back to (and then un-star them afterwards.) I use text search to find everything else.
I treat it like a giant single chat history.
I have never not been able to find an email when I need to, and I never miss a message.
Life is too short to waste time trying to maintain "inbox zero."
