As someone who has a similar issue with the MS teams/email divide...
Tldr: reduce reactivity and context switching. It will leave you exhausted and feeling like you are not making progress long term.
Chunk, at predetermined times for a set period.
Scan information channels in a set order first, broadly sort into topics. Go through each topic and extract relevant detail/actions into a separate personal log on the topic.
Tl:
One thing that is often overlooked is how this way of working puts you in to a hyper-reactive mode, taking you away from the things you had originally wanted to tackle at the beginning of the day. It is procrastination, it is your brain looking for an excuse to do something else. This will stoke the belief that, despite best intentions, you get distracted, can't work on the things you need/want to do and fail to make meaningful progress leaving you feeling tired and that you've fallen behind.
For me (read: maybe for you too, maybe not) what works is checking those channels at predefined intervals throughout the day (as you suggested) but having a prioritised list that you stick to in which ones you check, for how long, and follow that list each time. While going through, write a task oriented summary of the actions you need to take. If the information is more status/contextual/fyi on a particular thing, have a diary/log for that particular thing where you are updating you knowledge/understanding/the status of that particular thing.
For example:
I'm working on a complex project right now where there are 10 separate countries all doing similar but different things across several technology stacks. Most of this is over email, so things easily get lost in a sea of email headers and signatures. Similar but different issues in different countries get mixed up. It's hard. Even without ADHD. First I generally sort all emails into folders or with labels by topic. Then I'll go through each topic separately and copy out the relevant detail and append it to a running document on that particular thing with details of who said what and when.
You can do this low tech, but I like to use obsidian to markup and further link info on things/concepts/people/dates so I can search across it later.
I hope this helps someone.
And for god's sake, turn off ALL the notifications you can!
Put a note in your status starting 'if it's urgent, call'. This is an entirely reasonable request.
Good luck