APL (Dyalog Unicode), 74 49 45 bytes^SBCS

{⍵@(⌈x÷2)∘⍉∘(⌽⍵@(2/¨⍳x))⍣2⊢''⍴⍨2⍴x←≢⍵}(⊢,1↓⌽)

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APL (Dyalog Unicode), 74 49 45 bytes^SBCS

{⍵@(⌈x÷2)∘⍉∘(⌽⍵@(2/¨⍳x))⍣2⊢''⍴⍨2⍴x←≢⍵}(⊢,1↓⌽)

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-11 thanks to ovs

Explanation:

{⍵@(⌈x÷2)∘⍉∘(⌽⍵@(2/¨⍳x))⍣2⊢''⍴⍨2⍴x←≢⍵}(⊢,1↓⌽)
                                      (⊢,1↓⌽) ⍝ turn "abc" into "abcba"
{                                x←≢⍵}        ⍝ x is the length of that string (passed as an argument)
                           ''⍴⍨2⍴             ⍝ Generate a blank string of x times x
                        ⍣2⊢                   ⍝ Do twice:
 ⍵@(⌈x÷2)∘⍉∘(⌽⍵@(2/¨⍳x))                      ⍝ Update our blank string with our argument (the mirrored string):
              ⍵@(2/¨⍳x)                       ⍝ Add our element horizontally, replace with our (mirrored) argument
            (⌽         )                      ⍝ Rotate vertically
          ⍉∘                                  ⍝ Transpose (double rotate, vertical and horizontal)
 ⍵@(⌈x÷2)∘                                    ⍝ Add our argument vertically to the string

Since we're doing these transposes twice, we'll have rotated our image on all four quadrants.

APL (Dyalog Unicode), 74 49 bytes^SBCS

{(⌽∘⍉⍵@(2/¨⍳x))⍣4(⍉(⍵,1↓⌽⍵)@x)⍣2⊢''⍴⍨2⍴1-⍨2×x←≢⍵}

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APL (Dyalog Unicode), 74 49 45 bytes^SBCS

{⍵@(⌈x÷2)∘⍉∘(⌽⍵@(2/¨⍳x))⍣2⊢''⍴⍨2⍴x←≢⍵}(⊢,1↓⌽)

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-11 thanks to ovs

APL (Dyalog Unicode), 74 bytes^SBCS

{p←2/¨⍳≢⍵⋄m←⍵,1↓⌽⍵⋄m←⍵,1↓⌽⍵⋄⍵@p⌽⍵@p⊖⍵@p⌽⍵@p⊢m@(≢⍵)⍉m@(≢⍵)⊢' '⍴⍨2⍴1-⍨2×⍨≢⍵}

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APL (Dyalog Unicode), 74 49 bytes^SBCS

{(⌽∘⍉⍵@(2/¨⍳x))⍣4(⍉(⍵,1↓⌽⍵)@x)⍣2⊢''⍴⍨2⍴1-⍨2×x←≢⍵}

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-6 thanks to ovs