Short answer: AI is more capable than SVG.
EPS and PDF are final, compact, one way file format. Its purpose is to be consumed as a document, either for screen or for print. It is not intended as a 'working' document. Once the EPS/PDF is generated it's not supposed to be worked upon afterwards. For example, text boxes no longer exist in a PDF, just lines of ...
Possibly a bug.
When I repeat your steps, in the image print size (Image>Print size) the print definition has been reset to 72PPI (and since the size in pixels hasn't changed, this gives the strange print size).
Forcing the print definition back to 300PPI seems to fix it for good (doesn't change with later exports or edits).
PS: made a bug report
You can't open or edit an AIT file directly. It's a template file that has to be applied when opening a new document.
To get around this, you could open a new document based on a template, then afterwards save that new document as a new template.
Please check the documentation from Adobe on the use of AIT files:
Create a new document from a template
I wanted to throw out a shout for ORA (OpenRaster) format here for anyone who is looking. https://www.openraster.org/
This format likely does not support all photoshop specific features, but it aims to support the general representation of a layered raster graphics format with metadata in a very simple and reusable format for programmers to work with. All ...