Tl;dr: This Tampermonkey userscript automatically reads inbox notifications when it is opened instead of requiring one to press the Mark all read button.
I gave it the MIT License, and the source code is on GitHub.
A change was made to not automatically mark notifications as read (and require one to press a button). However... I personally prefer the old behavior of then being automatically read as soon as the inbox is opened, so I wrote a userscript to do that. See also this MSE answer suggesting an option to do that.
This userscript detects when the inbox button is pressed (by setting its
onclick* to a bit of code that simulates pressing the button to read all notifications)
*The SE inbox uses events not
onclick for the button that opens the inbox, meaning that the
onclick property is free for me to use
Tested with Tampermonkey on Firefox, although this will almost certainly work on Chromium-based browsers too