That button doesn’t specifically perform a right click. It is a button to open a menu, not necessarily right click. It just happens that right clicking in a lot of situations also acts as hitting the menu key. It’s super pedantic, but a lot of software still makes use of it and it sends a different command for stuff like scripting and macros.
Realistically it won’t make a difference since you have an unlocked bootloader anyway and you won’t be able to pass strong integrity with it unlocked regardless. It just makes using some apps a bit of a headache, but if you can deal with playing cat and mouse with safetynet fixes it’s not really much of an issue.
As far as apps, I recommend the gappsmod to get the Pixel dialer features and AdAway as a baseline, but it really depends on what you want to do with the device.