This variable hasUnsafeComments should be moved inside the fix as it is only needed then and it should be specific to the members being swapped.
In the following example it is safe to swap "b" and "c":

{
  // Comment for a
  "a": true,
  "c": false,
  "b": false
}.

I thought about this case as well, but reliably detecting only safe cases like this requires non-trivial comment association logic, and it’s easy to get wrong. So I’m not sure it’s worth adding that complexity.

You can use sourceCode.getTokenBefore/After with includeComments: true for each property and then do not fix if one of the four tokens is a comment (for getTokenAfter make sure that you skip commas with a filter):

const commentTypes = new Set(['LineComment', 'BlockComment']);

function hasComment(member, sourceCode) {
	const before = sourceCode.getTokenBefore(member, { includeComments: true });
	const after = sourceCode.getTokenAfter(member, { includeComments: true, filter: ({ type }) => type === ',');
	
	return commentTypes.has(before.type) || commentTypes.has(after.type);
}

This alias (prevMemberNode = prevMember) is unnecessary as fixes are eagerly executed (you can replace the references of prevMemberNode with just prevMember).

That alias is intentional. Without it, ESLint reports a no-loop-func error (Function declared in a loop contains unsafe references to variable(s) 'prevMember')

Oh okay, personally I would prefer an eslint-ignore as this is a workaround which trips up developers reading the code.
I don't feel strongly either way but can you please add a comment explaining why the alias exists?