Build me a castle Stairway!

05AB1E, 12 bytes

Code:

vDNúsÀ}\».B∞

Uses the 05AB1E encoding. Try it online!

Explanation:

v     }        # Length input times, do.. (N = iteration count)
 DNú           #   Duplicate and prepend N spaces
    sÀ         #   Swap and rotate one to the left
       \       # Discard the top of the stack
        »      # Join the stack by newlines
         .B    # Pad with spaces into a rectangle
           ∞   # Mirror the string

Jelly, 16 bytes

J’ɓ⁹⁶ẋ;"ṙz⁶Zm€0Y

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Of course, -1 using Jonathan Allan's ɓ!

Python 3, 89 bytes

x=input()
l=len(x)
for i in range(l):y=x[i:]+x[:i];j=' '*i;print(j+y+'  '*(l+~i)+y[::-1])

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-1 byte thanks to ovs

-1 byte thanks to Lynn