Hello @motivated_master9627
I hope you are doing well, and sorry for the trouble you had.
Please note that the Add Text tool under Edit a PDF adds text to the page content itself, it becomes part of the document, like editing the original text, not an annotation. That is exactly why it does not appear in the Comments List and why you cannot select and copy the boxes as objects to move to another file. Acrobat's edit-mode copy is oriented to within a document; page-content text boxes are not designed to be selected as a group and pasted into a different PDF.
And the Select Object tool you found under Rich Media is for interactive objects, form fields, links, buttons, and multimedia, not page-content text. That is why it does not grab your added text. It is not the tool for this.
Use the Comment tool's text box instead of Edit > Add Text. Those are annotations, so they:
Show up in the Comments List, and
Can be copied and pasted, including into another PDF.
The tool is Comment (All tools > Add a comment) > Add text comment / Text Box. To copy them across documents, the reliable method is to select the comments in the Comments pane, copy, switch to the other PDF, and paste. One known quirk worth knowing: when pasting a text box comment onto the page, do not click first to position it, just paste, then move it, otherwise it can refuse to drop. You can also move a whole set at once by exporting the comments to an FDF/XFDF file and importing them into the other PDF (Comments pane > Options > Export/Import Data File), which is ideal for reusing the same set repeatedly.
For text you reuse often, a Custom Stamp is even better: turn your boilerplate into a stamp (Comment > Stamps > Custom Stamps > Create) and drop it onto any PDF in one click, no retyping.
Please check these articles for more information:
https://helpx.adobe.com/acrobat/using/edit-text-pdfs1.html
https://helpx.adobe.com/acrobat/desktop/share-and-review-documents/review-documents/add-comments.html
https://helpx.adobe.com/acrobat/using/importing-exporting-comments.html
I hope this helps, and please reach out if you need any assistance.
Regards,
Anand Sri.