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Privacy Badger stopped using heuristic 4 years ago because it could be used to fingerprint you.
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Cookie autodelete simply does not work with Firefox’s Total Cookie Protection, which is enabled by default.
As of Firefox 86, strict mode is not supported at this time due to missing APIs to handle the Total Cookie Protection. Also as of Firefox 103, standard mode has also enabled Total Cookie Protection. Use ‘strict’ mode if using pre-86, use standard mode for versions 86-102, or from version 103+ use the custom configuration and set cookie to ‘cross site tracking cookies’ option (not the cross-site cookies).
https://addons.mozilla.org/fr/firefox/addon/cookie-autodelete/
You don’t even need an extension to automatically delete cookies, just enable privacy.sanitize.sanitizeOnShutdown
and privacy.clearOnShutdown_v2.cookiesAndStorage
. To add an exception: Ctrl+I>Permissions>Cookies>Allow.
Check Arkenfox’s extension page and the section about sanitizing on shutdown.