Will pages 09 doc's be readable on current pages version?

Yes they will. When planning your migration from the old Mac to the new one, please click Setup Assistant and Migration Assistant and follow the instructions for an easy, quick and reliable migration.

Usually, the current version of Pages will open Pages '09 documents but understand that the applications are substantially different in their implementation with entirely different document architectures. An unqualified "Yes" would be misleading to you.

In a nutshell, if the Pages '09 document, or the template upon which it is based, uses functionality missing or implemented differently in the current Pages, then either the document will not open, or the content will appear different than the original Pages '09 document. For instance, text box linking only goes forward in the current Pages as opposed to bi-directional in Pages '09.

You are encouraged to keep pristine backup originals of your Pages '09 documents and only attempt to open copies of these documents in the current Pages. Once opened, any attempt to change anything in that document will convert it to the current Pages document format and it no longer remains a Pages '09 document, nor can it be opened in Pages '09 on an older Mac. Although there is an Export To > Pages 09 option, it does not revert current document changes back to the originally opened Pages '09 content.

If you use Apple's Migration Assistant to restore user data from the 2013 iMac to the new Mac, do not migrate applications as they will all be incompatible with current Apple Silicon Macs. You can get the current Pages, Numbers, and Keynote from the Mac App Store.

Reference: Pages User Guide for Mac - Apple Support

Yes, they will. I continue to use Pages 4.3 & Numbers 2.3 on my Mojave Mac regularly & have no problems opening the files in the current versions on Sonoma.

Your welcome