How do I replace specific sequences of a sublist without changing the level of the list?

You can use pattern matching with BlankNullSequence

testlist //. {List[a___,1,0,1,b___] :> List[a,1,1,1,b]}

{{1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0}}

Another way

SequenceReplace[{1, 0, 1} -> {1, 1, 1}] /* Flatten /@ testlist

Inspired by @carl woll's comment

SequenceReplace[{1, 0, 1} -> Splice[{1, 1, 1}]] /@ testlist

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