In general, "was" can imply an ongoing effect, but it's heavily contextual. Generally it depends on how immutable the trait or characteristic of the person or thing in question is.
The jar was full of cookies.
could mean a few different things:
If this is a sentence as part of a larger story, it's probably just telling you about the state of the jar at the moment in time that the story takes place. The jar is probably important to the story in some way (see: Chekhov's gun) and may be involved in the subsequent events of the story. But there's nothing about the sentence that necessarily implies that the jar doesn't have cookies in it anymore. At the same time, it's going to be a boring story if nothing changes.
If this is a statement made in the present moment, it is probably to draw a contrast between the previous state of the jar and now -- implying that, in fact, the jar is no longer full of cookies. Otherwise, why make a statement about it at all? It hardly seems useful to point a trait like that.
This could also be read with a slightly accusatory tone, as in, "Well, the last time I saw it, the jar was full of cookies... [and now it clearly isn't, and one of you jerks is responsible!]." In that case it's definitely different.
The context clue is essentially how immutable or not the characteristic of the thing we're talking about it. A jar's state can easily change -- it's not hard for someone to take a cookie, presumably. So it would not be surprising if "was" describes something that is a change in this case.
On the other hand, something like
Fred was funny.
tends to describe something that doesn't change about a person -- their sense of humor. If you haven't seen Fred for years and years and are reminiscing, it's more like the first bullet point above; you're just describing Fred at a point in time, and there's no implication that he's not still funny.
"Funny", in other words, is not something that a listener generally expects to have changed about a person. Usually something more drastic about the person's life would have to change for "was" to imply a change, like they die or become incapacitated in a way that makes them no longer able to express a sense of humor. So "was" usually implies an ongoing effect here, rather than a change.
This property of the English past tense -- the ambiguity about whether the characteristic in question is still ongoing -- is often exploited to great effect for humor. For instance,
"I used to do drugs. ... I still do, but I used to, too."
-- Mitch Hedberg
Here Mitch Hedberg starts off with an admission that most English speakers would initially assume is about a characteristic which is no longer active -- namely, drug use. The joke is that he's subverting the audience's expectations.
Taking your other example between Joe and Sarah, no reasonable English speaker would ever say this:
Joe: [...] It merely implies that during some interval in the past, I evaluated the process of knowing you as good. I've said nothing about my current or future evaluations of the process, nor anything about whether the process itself continues or will continue.
because they would sound like an insane robot, hyper-evaluating all the possibilities at hand in the multiverse. So for your updated question,
In the strictest sense, which of Joe and Sarah is correct?
Sarah is certainly being much more reasonable than Joe is and is making perfectly fine assumptions (at least, up until the point where Joe sounds like a crazy robot).