page numbering

If you want display page infor in document, you can define a new Text Variable and set Type is Last Page number , prefix  is text before and suffix  is text after.

I don't quite understand your dilemma. What is the prefix "p-"? Literal text or what? Same for the suffix "-s"

In setting up sections and pages, InDesign is a little fussy: it wants you to have the section prefix before the page number. But it really doesn't care what you use as a suffix. You can use literal text, or a text variable, or whatever.  For example, for the first section created with the script below:

1. The following entry on A master page: A-Whatever (current page number followed by literal "-Whatever") shows as: A-1-Whatever on the first page.

2. The following entry on A master page: A-Test Doc (current page number followed by a File Name Text Variable that has a hyphen assigned as its prefix) displays as A-1-Test Doc on the first page. (Test Doc is the name of the InDesign file.)

Here's the script (AppleScript)

tell application "Adobe InDesign CC 2019"

tell document 1

make section with properties {name:"First", continue numbering:false, page number start:1, page start:page 1 of spread 1, section prefix:"A-", include section prefix:true}

end tell

end tell

I don't think that is possible even using the InDesign UI. Are you able to achieve this without scripting?

-Manan