Sort by file name directly after importing images?

If the only difference between these images is that they have different sizes (resolutions), but otherwise they retain their original capture data from the camera, these should still show in a systematic way after import (within the "Previous Import" view) since that sorts according to capture date and time. And that will normally (for most users) equate to filename order since cameras typically name the photos with a sequential number depending on the order in which they have been taken.

IOW, other things being equal, filename order and capture order amount to the same thing within most people's default use case. If the capture order that's seen is chaotic and arbitrary, then that suggests something arbitrary has happened to the starting capture metadata before import to LR. If the extant filenaming has some desired meaning so far as sorting, which is different than what original capture date would have equally well conveyed (if preserved) - then this has been given to the files before import to LR. In either case, it may be worth considering either a simpler workflow which calls on LR to carry out more of these processes itself - or else, a better behaved prior workflow which properly passes through camera info unaltered, so that LR can later make productive use of that.

When viewing the images from the Folders panel, Lightroom usually remembers my last used sort for that folder (filename in my case). However, the "last import" collection always seems to be stuck sorting by capture time.

As far as I'm aware, file size has no bearing on sort order in Lightroom. When images are imported Lightroom sorts them by capture time, and I don't believe there is a way to change that. I know, I prefer filename order as well. And I always have to remember to change the sort order after I performed an import. If there's a way to defeat that I'm not aware of it.