I’m not following the connections you’re trying to make.
No. が as a nominaliser (i.e. like modern の) is completely dead and survives only in specific fossilised expressions like the one you mention.
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Would the same phenomenon occur with words like 上手? Am I writing this correctly?
「私は泳ぐのが上手です。」
「他に誰が泳ぐのが上手ですか。」
「マキさんが泳ぐのが上手です。」