Old illustrator file rasterised and paths outlined when opened in latest v. - how to avoid this?

Open the original EPS in Text Edit and show us the first part of the header. That will show you what "version" of Illustrator created it, and a clue as to what compatibility it is, like so:

Anyway, everything in your screen grab points to this being saved as an older EPS version (i.e. my guess is before Illustrator 9). EPS does not support mesh and transparency effects without "flattening", which includes outlining strokes, and breaking up text into chunks, depending on the Transparency export setting. In fact, this is happening in any EPS version, even the most current 2020 compatibility. The default is Medium, (and most people don't even think about this setting) which does everything you are experiencing (e.g. stroke to outlines).

The difference in editabilty rests on what version of Illustrator compatibility setting was used, so the native Illustrator object structure would still exist in the file so you can reopen them and continue editing. Versions older than v9, do not support mesh and transparency objects in them, so will only open in the flattened form.

The other clue is that your text is broken up into chunks. This happens to older files saved with the pre-CS era text engine.

Is there anything you can do now? No, the damage has been done, unless you have .AI versions of those particular files around somewhere.

If you want to have one of us poke at the file, send it along.