Maybe your context is different, but all I can say is that I used to consider email to be something that you respond to when you get to it. Yet after enough complaints were raised against me I had to change that behavior and reply immediately even if it was just to say "I will look into this".

I am not personally upset if people don't get to my emails right away, because if I have anything actually urgent I'll get a Teams message out to the person who I know can handle it. (That does change a bit if the communication to to an external vendor in which case it's going to their support team who I do expect to respond promptly).

That was also me, but it became unsustainable. I got a lot of reader mail and had to update my contact page to redirect some of it to other experts.

I stopped treating my inbox as an obligation and I reply at my own pace. I still give each email as much consideration as I can, but I no longer feel that it’s required. Some emails go unanswered.

I am slowly working on setting boundaries, especially in response to expectations that I did not opt into. It’s indeed a very contextual reply.