Witcher is a silly thing to use as your first example, it's a made up word for a translated book. I can't think of another word that behaves like that. Making a mountain of a made up molehill. A Molehiller, I would call you.
I've always thought of it as "Xer" = "someone who Xes". X should be a verb. Builders build. Welders weld. Miners mine.
In the case of birder, birding is an activity, which I guess makes "bird" a verb ("to go birding"). "Witcher" was made up for the setting, but I guess "witch" is similarly a verb there.
What is "birding"? According to dictionary, it's breed, catch, or watch. Fishers fish, right? What is "to fish" really, though? To swim? To be a fish? I mean, you can't extrapolate it from the common verb as a rule, because that doesn't apply to "birding", does it?
So no, I don't think your over-simplification works.
It's not an over-simplification. This is literally just what the -er suffix does, besides the unrelated usage to make comparisons like "louder". Look up "agent noun" for more info.
What is “birding”? According to dictionary, it’s breed, catch, or watch.
The common usage is to watch birds. The extension of the verb "bird" into "birder" is also commonly understood to mean someone who watches birds.
What is “to fish” really, though? To swim? To be a fish?
What? It means to catch fish. I've never heard any other meaning? Again, it's not based on what a fish does, it's based on what the verb "fish" means, which is to catch fish.
I mean, you can’t extrapolate it from the common verb as a rule, because that doesn’t apply to “birding”, does it?
Ignoring the fact that "bird" is a verb with a fairly well-understood meaning, the reason "birder" or any other -er words are ambiguous is because the verbs are ambiguous. Words have multiple meanings... that's just something that they do. That doesn't change the overall rule that "birder" means "someone who birds", it just means you have to figure out which meaning of "bird" (as a verb) it's using.
Yeah and wiedźma has the same root as wiedzieć and to know in proto indo-european.
He's a man of knowledge. About killing things out of this world.
Canonically witchers world coexists in our own multiverse and was similiar to our own reality, but thanks to some bonduary bluring between cosmic realms got tainted hundreds years ago by otherwordly magic and monsters.
So the whole witcher, wiedźmin name just indicates knowledge, an is likely a name given to them by common people instead of being an endonym.
I was under the impression that Witcher is to be interpreted as the male form of Witch - a Witchman, basically. I think they even call Geralt a Witchman a few times in the games, come to think of it.
-er is the agent suffix in English. Effectively it turns words into those who do something related to that word.
Hawk > Hawker = One who "hawks"
Run > Runner = One who "runs"
In principle this implies the existance of a verbal form of the root word, such as the two above examples.
Witcher, as used by the fantasy series, is a weird one because it's actually not related to the agent suffix.
The Polish title of The Witcher is Wiedźma which just means "witch". When it was translated to English they adopted "witcher" as a masculine form to the oft feminine "witch" by using the ability for the -er suffix to indicate a profession or association with a noun in English i.e. Cash > Cashier, someone who handles cash/payments (actually derived from french with the -ier suffix, but point still stands). In the cass of Witcher it is one who works as/with witches or else one who is associated with Witches.