Hi, I'm the author of this add-on. You might want to read the FAQ entry "Q: How is this different from disabling 3rd party cookies and installing Adblock?". Firefox's new 3rd party cookie policy is actually weaker than disabling them outright, so this will not change anything.
Back in the day, Firefox experimented with making third-party cookies session-only, but I believe this option was disabled because some websites using third-party login cookies required users to login every session.
Have you run into any problem websites with self-destructing cookies?
Disabling 3rd party cookies has never broken a single site for me. I've heard that some banks require them, though.
As for Self-Destructing Cookies: it's a pretty drastic measure. Considering this, it's surprisingly compatible. Among the sites that I frequent, not a single one stopped working. Inter-domain transaction - e.g. a shop forwarding you to Paypal and back - used to be a problem, but the latest version has a heuristic for that. Still, I'm pretty sure that some people will experience fallout. You can work around that; SDC has numerous functions that can help in such cases (pause, undelete, whitelist for session).
it should, it blacklists all sites by default to not persist cookies at all beyond having the window open.