Q: But how about continuity? And which one is “canon”?
A: Whichever the readers want it to be.
Most readers who are concerned about continuity and canonicity would automatically consider the work of the original author as the “Prime Reality”. Everything else are in “Other Realities”, or a branch of the timeline, or a parallel world.
The beauty of this is that, for literary works where canonicity and continuity is important, the original author can suddenly declare this work is canon and/or part of the continuity. Those who did not read that, will suddenly start to read that work.
It creates an ecosystem where authors of a #SharedWorld can help each other.
In any case, an #author who dedicates their work in the Public Domain; or use an Attribution and/or ShareAlike license, more likely than not already understands how canonicity and continuity plays a role for their own work. These authors would have set their own guidelines already.
For example. Author A prefers to have complete control over the “Prime Reality”. That works fine. Most readers prefer this, since this what we're used to. At the same time, it doesn't invalidate derivative works; AND the Author A can also reuse derivative works.
Author B on the other hand declared that there is no “Prime Reality”. It is up to the readers to decide which particular path of the story they prefer. It could be primary author's (Author B), or it could be Author C, Author D, and so on.
Literally, there is no fan fiction in this setup. What would have been fanfiction are simply different realities (timeline/worlds/paths).