I have been trying to fix this for a day or two now, but nothing I do seems to work. Suddenly and without any real cause that I can see, the back end and the front end of my stylus are registering as the same brush. When I check the tablet tester menu, it says that it detects the 'Eraser brought near/taken away' and 'Pen tip brought near/taken away'. What can I do to switch the back end to being a separate brush? I really dislike having to switch my pen size whenever I want to erase something.

On a new session, krita forgets what the previous use of the 'eraser end' of the stylus was.
You have to use it to select the brush preset you want from the brush presets docker.
Is this what the situation is?

Or do you mean that even if you use the 'eraser end' to select a particular brush preset from the brush presets docker, it doesn't actually do that?

Even if I select something else, it just acts like both ends are the same.

I've no idea why this may be happening.
If you go to https://krita-artists.org/ (sign up and sign in needed) there may be someone there who can give better advice.
It's also a forum that has very convenient image uploading facilities.

In the Brush Editor (F5), the Eraser Switch Size option is usually selected by default so you can set a different size for the tip when you have Eraser Mode enabled via the icon in the Toolbar.