Last week, I shared a few thoughts about turning off notifications for your own peace of mind.
I promised that I'd share my own set-up for managing inboxes, in case it's helpful for anyone else.
Before I do, note that this is a work in progress. My goal with all of this is to not feel like I'm constantly working. My way may not be the best way for you, so please do whatever works best in your situation
Phone
I use the Before launcher to manage notifications and as a simple homescreen on my phone (free/$6; I paid the $6 one-time upgrade after trying it out for a while because I like to support folks making good stuff, but the free version works great. I didn't really need to upgrade.) I have most notifications turned off. I also turn off sound most of the time unless I am expecting a call. With a few exceptions, I don't see new activity in apps unless I manually check them.
I separate work and personal email into two completely different inboxes. For work email, I pay for Protonmail (just the personal plan). I route almost all notifications through email and directly into specific folders, so they don't land in my inbox.

I do this by setting up filters. So, anything from Practice Better gets filtered directly into the PB folder without landing in my main inbox. Anything from MailerLite goes into the ML folder, etc. If I'm taking a class with heavy email notifications, I create a folder for the class and route emails there. I manually add newsletter sender emails to the filter for the "Ads and Newsletters" folder, which is a bit of a pain on the front end, but then they automatically go into that folder, and I only see them if I check there.
Process
My new process is that I check work email on work days 3x/day for 15 minutes at defined times, and then I close out the window. With the window closed, I don't see any new messages until the next time to check. My filtering system means that new messages in my work inbox mostly consist of personal messages that I actually want to/need to read. This system is working well for me, and cuts down on the feeling that I've always got messages that need a reply.
I skim through the ads/newsletters folder once per day or so, deleting after reading or if I decide not to read.
So, there it is. I hope this is helpful and not overwhelming. I'd love to hear more about your process or any tips/tricks you've developed to make messaging more manageable.
Take care,
Camille