The Ikea instructions for the non-square Kallax (3x4, 2x4, 2x1) state that you can use them any way up with a max loading of 13 kg per shelf.
The larger ones are recommended to be attached to the wall, whichever way round.
With the square ones it shows long shelf horizontal (it's square, why not)
Some of the smaller ones can be wall mounted and mounted on wheels. But not the bigger ones.
Craig's link above is not to a Kallax, it is the discontinued Expedit, and and is a 5 x 5 one. They did have a which way round.
(Which the 5x5 and 4x4 Kallax may have also - but who cares as they are the same size so you can easily do that)
13 kg - take a typical LP to be 190g LP and sleeve - that is 68 LPs. Which was the calculation I did in my head when ordering the shelves whilst sat on a tram.
I've just measured three full bays on one of my Kallax... ...erm - which is the plural of Kallax? Anyway...
Bay 1 - 58 items, 20 kg (344g per item) - a lot of heavyweight double albums and some triples
Bay 2 - 64 items, 20 kg (313g per item) - slightly fewer heavyweight double albums
Bay 3 - 69 items, 20 kg (290g per item) - mostly 60s/70s/80s single albums, some180g and 200g
So the risk there is that I'm overloading each shelf with what fits. And they are not rammed in there.
(Picture above, second row from top, bays, 2,3 and 4 - Back to mine unmixed to Miles Davies).
It does seem unstressed when flexed.
This also assumes my kitchen scales are accurate. If another Kallax owning pink fish would attempt a weigh with known accurate scales that might help.
I do have a lot of 180g double albums in heavy sleeves. YMMV.