Is there any attribute which can be accessed across adobe applications?

@Test Screen Name said: "EPS has nowhere to store metadata such as label/ID for graphic elements."

Hm…

One could include code written in Encapsulated PostScript plain text that can be placed and embedded on top of every element on an InDesign page. The embedded EPS files could contain pdfmarks code that itself will be converted to PDF comments if the page will be printed to PostScript or exported as EPS and later distilled to PDF with Acrobat Distiller.

That's the one part on the InDesign side that can be done to include comments to an exported EPS file.

The question is if Adobe Illustrator is able to read the comments. Ask this in the Adobe Illustrator forum.

Or perhaps you could write a parsing piece of code for Adobe Illustrator that could retrieve the comments from the EPS before Adobe Illustrator will open it.

Notes:

Acrobat Pro or Adobe Reader could read and show the comments if the EPS was distilled to PDF.

However, for this you need Acrobat Pro installed, because Acrobat Distiller is installed together with Acrobat Pro.

See into PDF Marks:

https://opensource.adobe.com/dc-acrobat-sdk-docs/library/pdfmark/index.html

https://opensource.adobe.com/dc-acrobat-sdk-docs/library/pdfmark/pdfmark_Syntax.html

And also this thread at the Adobe InDesign Forum from 2016 that I edited today:

https://community.adobe.com/t5/indesign-discussions/pdf-options/m-p/8682617#M29013

What's more:

The comments done with pdfmarks are something like an "extra layer".

They are not tied to native objects on an InDesign page directly.

They are not something like the "label" property of ExtendScript for InDesign.

Regards,
Uwe Laubender
( Adobe Community Expert )

EPS has nowhere to store metadata such as label/ID for graphic elements. So it is not just a question of writing code; the info cannot be stored in your proposed workflow.

Forogot to mention; exporting eps from InDesign and opening in Illustrator