Does "know more about something" really mean "more" (implying that one already has some prior knowledge) or just a customary phrase

The phrase from the outset doesn't imply that the readers have no prior knowledge at all. In fact, the definiteness of the phrase this remarkable people shows that the people in question have already been mentioned, and so the reader does in fact know something about them (at least that they exist, if nothing else).

The phrase from the outset refers to the beginning of the story, but that doesn't necessarily mean the very first sentence. Especially in a text of the size of The Lord of the Rings, several first chapters still count as 'the outset'.

I don't have my Tolkein right in front of me, but I would interpret this to mean that Tolkein has already given a very brief description of the people of Middle Earth (or maybe just Hobbits) and postulates that many readers might want to know more right away rather than jumping right into the story narrative.
I interpret "from the outset" to mean here, at the beginning of the story, and not necessarily implying that absolutely no information has yet been provided about the people of Middle Earth. On the contrary, as you point out, the "more" would indicate some small amount of information has already been provided.

"Concerning Hobbits", the first section of the prologue of The Fellowship of the Ring, from which the quotation in the question was taken, begins:

This book is largely concerned with Hobbits, and from its pages a reader may discover much of their character and a little of their history. Further information will also be found in the selection from the Red Book of Westmarch that has already been published, under the title of The Hobbit.

Then there's one more sentence describing very briefly the nature of The Hobbit, and then the quoted sentence.

So in this context, "know more" means know more about Hobbits than what is learned from The Hobbit.

If you changed the sentence to "many, however, may wish to know about this remarkable people from the outset" it would make the mention of The Hobbit in the two prior sentences unnecessary, or confusing.