directly change the background value of a SparseArray?

You can change the background using replacement; here making the background "x":

s = SparseArray[{1, 10} -> 1, {1, 10}, a]

s /. (sa : SparseArray)[a_, b_, background_, d_] :> sa[a, b, "x", d]

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s = SparseArray[{1, 10} -> 1, {1, 10}, a];
s2 = SparseArray[s["NonzeroPositions"] -> s["NonzeroValues"], Dimensions[s], b];

A slightly slower way using ArrayRules:

s3 = SparseArray[Most@ArrayRules[s], Dimensions[s], b];

I haven't tested these on later versions.

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