No, in current releases you shouldn't rely on "Delete cookies and site data when Firefox is closed" as this is merely a shortcut to makes changes to the "Clear history when Firefox closes" settings. If you place a check on "Delete cookies and site data when Firefox is closed" then this merely makes changes to the "Clear history when Firefox closes" settings (Cookies and Offline website data gets enabled), so if you undo those settings then you prevent Firefox from clearing the cookies on exit. Just make sure not to clear the "Site settings" as this removes/clears the exceptions.

You can use these steps to make a website recognize and remember you.

• create a cookie allow exception with the proper protocol (https:// or http://) to make a website remember you

You can check that you aren't clearing important cookies.

• using "Delete cookies and site data when Firefox is closed" to clear cookies keeps cookies with an allow exception
  in 102+ version toggling this setting makes changes to the "Clear history when Firefox closes" settings and those settings prevail
• using "Clear history when Firefox closes" in Firefox 102+ honors exceptions and keeps cookies with an allow exception, previous versions removed all cookies

Make sure to keep the "Site settings".

• clearing "Site settings" clears exceptions for cookies, images, pop-up windows, and software installation and exceptions for passwords and other website specific data

• Settings -> Privacy & Security
  Cookies and Site Data: "Manage Exceptions"
• Settings -> Privacy & Security
  Firefox will: "Use custom settings for history":
  [X] "Clear history when Firefox closes" -> Settings

Thanks very much for the thorough response. I cannot say that I understand your response well enough yet, but I will work on it. I am greatly puzzled that this level of complexity appears in software in theory designed by users, or at least highly influenced by them. The cookie controls greatly need streamlining and simplification in my view. I may come back with questions.

OK, I think I got it now. The key point is under History to check the box in Clear history when Firefox closes, and then under the settings box for this also uncheck cookies and uncheck site data, leaving the rest checked, so cleared. And doing this in History unchecks the box for Delete cookies and site data when Firefox is closed. The net result which I can confirm on my PC is that cookies are cleared when closing, except for the Manage Exceptions list I create under Cookies and Site Data. Do I have this correct now? Hopefully this functional improvement can be followed up with a more, in my view, logical user interface, maybe just one section "History including cookies and site data", and having the exceptions and manage data lists there. So no more have two confusing sections not even adjacent on the settings page for privacy, with both addressing cookie management and history management in overly complicated ways. Do you agree with this type of suggestion?

In earlier Firefox versions you removed all the cookies including cookies with an allow exception when you select this in "Clear history when Firefox closes" and you needed to use "Delete cookies and site data when Firefox is closed" instead to retain cookies with an allow exception. In Firefox 108 this got changed and "Clear history when Firefox closes" honors the allow cookie exceptions. They decided to keep "Delete cookies and site data when Firefox is closed", but made it modify the cookie setting in "Clear history when Firefox closes". For clarity, best is to ignore the "Delete cookies and site data when Firefox is closed" setting and only use the "Clear history when Firefox closes" settings as that is what matters.