The rules don’t say
This is not defined anywhere in the rules. The DM is just going to have to make a ruling every time it comes up. They can be consistent about it, or decide on a case-by-case basis (probably better), but they aren’t going to be able to just look it up.
In English, the word “extra” implies being on top of something existing, but the “something existing” is not necessarily the same thing you are getting “extra” of. Within the rules, it is quite plausible to use “extra” as shorthand for “stacking with whatever you’ve already got, if any.” Or it is also well plausible that it means “increasing what you’ve got, if you’ve got it.” But the rules do not tell us which of the two we are “supposed to” pick.
Looking through the rules, we have basically three general scenarios for the use of the word “extra.”
Many of the uses of “extra” certainly are in situations where under the rules you must already have whatever is being augmented before you even encounter the word itself.
Many others are written in a similar manner, where usually you would have to have something there, but there are exceptional situations where you can get the “extra” effect without having the base value.
Others, there isn’t even anything in particular that suggests you could only get the “extra” effect if you had a base effect to build off of, except possibly from the word “extra” itself.
These different situations could plausibly be ruled differently. For that matter, concerns about balance and appropriateness should also be weighed by the DM.
This is part of a broader class of ambiguity in the rules, where something seems implicitly assumed in the rules and it’s unclear if something that breaks those assumptions should cause the results of those assumptions to be voided. The quintessential formulation of this kind of problem is when the rules say something like “you get X, because Y,” assuming Y to be true—if Y is untrue, do you no longer get X? This is not at all clear.
I would point out, however, that numerous places in the rules are more careful about this, and don’t rely solely on the word “extra.” Any of the “1.” cases, for instance. Also most prestige classes that advance something about another class, which go out of their way to emphasize that you must choose an “existing” class. Does the lack of such careful wording imply anything? Impossible to say, but it’s plausible to me, anyway.
Finally, remember that the context you are quoting was a rules-as-written discussion. I will always favor reporting the rules-as-written as “ambiguous” when there is any discussion to be had beyond rather-strict logic. The point of the rules-as-written is to eliminate subjectivity and personal opinion, and anything that needs discussing is something that is going to come down to subjectivity and personal opinion.