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"

The settings here prevail:

• Settings -> Privacy & Security
  Firefox will: "Use custom settings for history":
  [X] "Clear history when Firefox closes" -> Settings

Oh this is ridiculous, far too complicated. Turning delete cookies and site data when firefox is closed to clear cookies keeps cookies with an exception but in version 102+ toggling this setting makes changes to the clear history when firefox closes settings and those settings prevail!? Could you please streamline this so that there is one entry to make, and making that adjustment will provide a prompt to automatically override any other settings which will prevail so that the outcome is achieved? This is driving me mad, enough to ditch Firefox.

It has been streamlined already. Are the site exceptions being remembered across restarts? Make sure you aren't clearing "Site settings" where the exceptions are stored.

"Delete cookies and site data when Firefox is closed" by itself doesn't clear data but makes changes to the "Clear history when Firefox closes" settings and that is what matters.

@zeroknight - Typing in 'site settings' to zero in on that setting and unchecking 'cookies' and 'site settings' in that 'site settings' box has done the trick. Thank you so much.

I appreciate your help @zeroknight, particularly with the plain english. @cor-el thank you also, though, I must admit I found your answers complicated and could not understand them completely.

May I say that this could be done more simply; there are plenty of people who are not tech savvy, that would have no idea how to do this. Surely a prompt could be shown when adding a cookie exception to ask if you want to modify the other necessary settings, given that the cookie exception will FAIL without these extra adjustments. Alternatively, if the extra adjustments are necessary for a cookie exception to function correctly, then by simply adding a cookie exception perhaps the other adjustments could be applied automatically. Either way, it would streamline this further, and avoid frustration and confusion.

Man I hope this thread helps someone else!