You're either being pedantic over wording, intentionally difficult, or there's a language barrier. I can't decide which.
This has nothing to do with the 65816's direct page or stack. You can move those around
TO ANY ADDRESS within bank $00. Nothing stops you from doing
rep #$30 / ldx #$1234 / txs / lda #$FFF0 / tcd -- sticking the stack in the middle of the RAM region, and sticking direct page in ROM in the vector area. Is it practical/helpful? Probably not. But nothing stops you from doing it. CPU will do what you tell it.
Said "8K limit" (your phrasing) -- that is, the only RAM in bank $00 being between $0000-1FFFF -- is a result of the SNES memory map, not something specific to the 65816, direct page, or the stack.
Here is mode 20 and mode 21, and
here is mode 25.
I'm going to repeat myself one more time, and that's it: the "8K limit" (your phrasing) is a result of the SNES memory map, i.e. Nintendo's choice, and has nothing to do with the CPU (re: direct page, stack, etc.). You can move D and S around wherever you want in bank $00.
If you want to access the 128KB of RAM in banks $7E and $7F, you either a) switch banks by changing the B or DB register (which term varies per person; i.e.
phb/plb) and use 16-bit addressing, b) use 24-bit long addressing, c) use a cartridge that has SRAM on it and mode 21 (the first 8KB of SRAM will be mapped in bank $00 from $6000-7FFF, in addition to normal console RAM being at $0000-1FFF -- i.e. you now have 16KB of RAM to play with and can
lda #$6000 / tcd or
lda #$0000 / tcd to your heart's content), or d) invent a time machine and lecture Nintendo. Those are your options. :-)