Are you WFH? This sounds like someone (not unlike our dear PM) who believes that if you're working from home you are clearly skiving. No doubt any time you don't respond within a microsecond to his email or Teams message, he feels vindicated.
On the lunchtime issue, make sure you set your Teams status message to 'I've popped out to grab lunch' and tick the box that means it will display right above the message box for anyone who tries to contact you. Definitely set your status to 'Do Not Disturb' when you need to focus on work.
I definitely would be tempted to have a stock response to his email as @Crazylazydayz suggests - 'received, thank you'.
Another good technique, assuming you're using the Outlook desktop client rather than Outlook in a browser, is actually to click 'work offline'. This means you won't receive or send any emails. You can then deal with a batch of them and reconnect at the end of a session, whizz them all off and download the next lot, disconnect again until you're ready. If he challenges you on this say you've seen it as a great productivity tip on YouTube (that's where I got it from!).
In these one-to-ones, I'd maybe also be explicit 'I'm going to be offline for 2 hours this afternoon whilst I complete task <a> and I will check email after that'. Force him to object to your face. But fundamentally yes, I would look for another role pronto.