What I mean is that even after having rasterized the layer and dragging the selection rectangle to encompass all of the pixels in the new layer (which used to be text but is now rasterized so should be the only pixels in the layer that were put there by the user), It still forces me to see what gets selected as a rectangle containing the text rather than the collection of individual pixels that look like text (i.e. the rasterized stuff). In Photoshop, after rasterizing and using selection rectangle to completely contain the newly rasterized text, using the move tool would collapse the selection down so that the selection outline "clung" to the edges of the text rather than creating some rectangle that contained the text pixels. That makes sense because I just told it to rasterize the stuff - so why is it still treating it any different than any other collection of random pixels? I don't want to select a rectangle that contains the text. I only want to select the text. Any pointers?

In Krita if you select something, the selection stays the same even if the actual content is smaller. You can see the same behaviour when you just draw a dot and then make a huge selection around it. Also selection isn't on a particular layer (unless you're using a local selection), but it's global (when you switch layers, the selection stays the same; you can actually see it if you turn on Global Selection Mask showing).

Yes the move tool will always show an effective bound of what you move, by stripping all fully transparent pixels.

If you want to only select opaque pixels, there's a special set of "Select Opaque (...)" functions, e.g. you can reduce your rectangle to only opaque pixels with "Select Opaque (Intersect)". That way you can easily cut your text shape out of some other paint layer for example.
Note that semi-transparent pixels will be "partially selected". If you don't want that, you could apply a threshold filter on the (global) selection mask to get hard edges (not sure if there's a more convenient way...)