Approved but made a couple of changes during moderation:
-Some map16 tiles were wrongly assembled, which made the top of the mountains look a bit incorrect (sharper than they should), I fixed them
-There was a missing shade on one 8x8 tile, corresponding to the interior of the mountain, I fixed it
-Two of the mountain dots were a bit incorrect (missing some x/y flips to look as they do in the original game), I fixed them
-Added an alternate version of the background in a separate level, without the third mountain, just for convenience (also moved both sample levels to other level numbers)
-Changed LT3 destination to "Under Status Bar" as the tilemap is easily workable to avoid using a sprite status bar (making the "Start of Layer 3" option nonoptimal), and it's also the standard option full layer 3 tilemaps should use. Keep this in mind for futures layer 3 submissions, if you do.
-Changed pics to illustrate better the changes (particularly the restored status bar in the in-game pic, the updated map16 tiles on the map16 pic and the actual usage of the layer 3 tiles on the 8x8 editor, as they use LG4, not LG3)
-Not an edit, but chosing using palette 7 for the background is a weird choice given the few colors it uses. Consider using palette 0 or 1 next time, though your choice isn't really incorrect
That said, managing SMAS:SMB backgrounds is certainly something, as they use dynamic tilemaps that updates on level scroll, unlike static tilemaps that just loop over and over (indeed like in SMW, but in a lot of more games too), which is the reason I included a new sample level, but certainly it won't cover all the versions in the actual game (which also applies to layer 3). Fortunately, the tiles are very easy to manage in order to replicate all of them or even original ones, so it's up to the users, but won't be surprised if this is eventually updated with more sample levels/tilemap to add more alternatives.
That long text aside, good rip! Just be careful about these small mistakes I mentioned.