Python, 74 bytes (@DialFrost)

f=lambda n,m=0,p=-1:n and((*range(m,n),),*zip(*f(2*n-m+p,n,~p)[::-1]))or()

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Old Python, 76 bytes

f=lambda n,m=0,p=-1:n>m and((*range(m,n),),*zip(*f(2*n-m+p,n,~p)[::-1]))or()

-15 by reversing order of recursion.

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Old Python, 91 bytes

lambda n:g((n*n-1,))
g=lambda*s:(l:=s[0][0])and g((*range(l-len(s),l),),*zip(*s[::-1]))or s

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Builds the spiral from inside to out by recursively rotating 90° and adding a row on the top.

Python, 73 bytes (@ovs)

f=lambda n,m=0,p=-1:n*[n]and((*range(m,n),),*zip(*f(2*n-m+p,n,~p)[::-1]))

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Old Python, 74 bytes (@DialFrost)

f=lambda n,m=0,p=-1:n and((*range(m,n),),*zip(*f(2*n-m+p,n,~p)[::-1]))or()

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Old Python, 76 bytes

f=lambda n,m=0,p=-1:n>m and((*range(m,n),),*zip(*f(2*n-m+p,n,~p)[::-1]))or()

-15 by reversing order of recursion.

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Old Python, 91 bytes

lambda n:g((n*n-1,))
g=lambda*s:(l:=s[0][0])and g((*range(l-len(s),l),),*zip(*s[::-1]))or s

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Builds the spiral from inside to out by recursively rotating 90° and adding a row on the top.

Python, 76 bytes

f=lambda n,m=0,p=-1:n>m and((*range(m,n),),*zip(*f(2*n-m+p,n,~p)[::-1]))or()

-15 by reversing order of recursion.

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Old Python, 91 bytes

lambda n:g((n*n-1,))
g=lambda*s:(l:=s[0][0])and g((*range(l-len(s),l),),*zip(*s[::-1]))or s

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Builds the spiral from inside to out by recursively rotating 90° and adding a row on the top.

Python, 74 bytes (@DialFrost)

f=lambda n,m=0,p=-1:n and((*range(m,n),),*zip(*f(2*n-m+p,n,~p)[::-1]))or()

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Old Python, 76 bytes

f=lambda n,m=0,p=-1:n>m and((*range(m,n),),*zip(*f(2*n-m+p,n,~p)[::-1]))or()

-15 by reversing order of recursion.

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Old Python, 91 bytes

lambda n:g((n*n-1,))
g=lambda*s:(l:=s[0][0])and g((*range(l-len(s),l),),*zip(*s[::-1]))or s

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Builds the spiral from inside to out by recursively rotating 90° and adding a row on the top.

Python, 91 bytes

lambda n:g((n*n-1,))
g=lambda*s:(l:=s[0][0])and g((*range(l-len(s),l),),*zip(*s[::-1]))or s

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Builds the spiral from inside to out by recursively rotating 90° and adding a row on the top.

Python, 76 bytes

f=lambda n,m=0,p=-1:n>m and((*range(m,n),),*zip(*f(2*n-m+p,n,~p)[::-1]))or()

-15 by reversing order of recursion.

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Old Python, 91 bytes

lambda n:g((n*n-1,))
g=lambda*s:(l:=s[0][0])and g((*range(l-len(s),l),),*zip(*s[::-1]))or s

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Builds the spiral from inside to out by recursively rotating 90° and adding a row on the top.