How did 所以 semantically shift from "what one uses" to mean "consequently"?
This is easier than it looks.
As Wikitionary says, 所 is a verbal prefix that reinforces the verb's agentive value. Usually the presence of 所 doesn't change the meaning of the sentence, but it marks a verb used as noun modifier with 的, and suggests that the modified noun is what receives the action Zdic also explains it clearly: &quot;用在动词前，代表接受动作的事物&quot;. That's basically the definition of grammatical patient.
As an example:

我知道的事情 the things I know
我所知道的事情 the things which I know

The meaning of the second example with 所 is essentially the same, and the English translation actually does not differ. But 事情 is now marked as the patient of 知道, the role of 知道的 as a noun modifier is stressed, which you can render in English with an additional relative pronoun (which, that, etc.).
So as a standalone, the construction 所 + V + 的 is often translated as &quot;that which is V&quot;, and that is the passive participle Wikitionary talks about.
Now 以 in Chinese is a bit harder to fully understand for new learners, because it doesn't have one single translation in English. According to the context, it can be rendered as &quot;for&quot;, &quot;as&quot;, &quot;in order to&quot; &quot;to take/use&quot;. Once you get very familiar with how 以 is used, you might find a common denominator, close to &quot;to take as&quot;.
So if you put those two together 所以 is literally something like: &quot;that which is taken as&quot;, which shifts naturally to &quot;therefore&quot; -&gt; &quot;consequently&quot;.

因为我不舒服，所以我不想出门
I'm not feeling well, [that which is taken as = therefore] I don't want to go out