My notes from my iphone x did not transfer to my new iphone 13, The iphone x was stolen so I do not have it. How can I get my notes that I had saved on that old phone?

Then you were not using iCloud Notes. If you restored a backup and did not get the Notes, then they must have been in a mail account you were using. Check your mail accounts and see. You may need to log into your mail accounts on a browser to check that first, then if you determine which account it was, go back to Settings>Mail>Accounts>select that mail account and turn on the Notes switch.

If that does not work, and they did not appear when you restored from a backup, then they would seem to be lost. How did you transfer all of your content, by restoring from a backup?

How were you managing your Notes? Were you using iCloud Notes, or Notes on your iPhone? Were you using a Mail program to manage the Notes? If iCloud or Notes in a mail program, you need to turn them back on again. If you were using Notes on your iPhone, they would come from your backup. If using iCloud, go to Settings><your Apple ID>iCloud, and turn on Notes. If a Mail program, go to Settings>Mail>Accounts, click on the mail account that you were using for Note, and turn the switch for Notes On.

Why do you say they do not appear to be backed up to iCloud? If you restored from a backup and you were using the section, On My iPhone for Notes, they should have been backed up. Do me a favor and log into www.icloud.com, sign in with your Apple ID, then click on the icon for Notes and see if your Notes are there. If they are, to get them back on your phone go to Settings><your Apple ID>iCloud>Notes and turn the switch on.