You need to check this in the "Clear history when Firefox closes" settings as that is what matters.

• Settings -> Privacy & Security
  Firefox will: "Use custom settings for history":
  [X] "Clear history when Firefox closes" -> Settings
• https://support.mozilla.org/en-US/kb/delete-browsing-search-download-history-firefox

• using "Clear history when Firefox closes" in Firefox 102+ honors exceptions and keeps cookies with an allow exception, previous versions removed all cookies
• clearing "Site settings" clears exceptions for cookies, images, pop-up windows, and software installation and exceptions for passwords and other website specific data

Are all cookies being retained across sessions or only some? If you click on "Manage Exceptions", do you see any sites listed there?

Are you closing all Firefox windows? Quit from the menu (Ctrl+Shift+Q) to make sure it properly exits.

Does it still happen with all your extensions disabled?