The Hobbit is what?

[Tuor of Gondolin]

I imagine if an elf was asked he would say both no and yes.

It was originally written, of course, as a child's story originally
unconnected to greater Middle-earth,

...my mind on the 'story' side is really preoccupied with the 'pure' fairy tales or mythologies of the Silmarillion, into which even Mr Baggins got dragged against my original will...

Letters # 31

...not until the book was finished and published-indeed not until he began to write the sequel-did he realize the significance of hobbits-and see that they had a crucial role to play in his mythology. In itself The Hobbit began as merely another story for amusement. Morover it nearly suffered the fate of so many others and remained unfinished.

Biography (HC), p. 176-177.

So it rather depends on ones perspective whether to view it as originally
conceived or as later incorporated (philosophically and some crucial elements)
into Middle-earth mythology.