As others have noted, yes, the word "free" has multiple meanings, and so in some cases it may be necessary to add additional words to make clear which meaning is intended. (Of course this is true of many words in English, and I suspect in other languages.)
There is little ambiguity in this case. We surely do not mean "politically free", as bars of soap are rarely kidnapped and forced into slavery. :-)
There might be an ambiguity if you were talking about people in a place where slavery is practiced. Like, does "Robert is free" mean that Robert is no longer a slave, or does it mean that he is a slave who is being given away for free as part of a promotion being run by the slave dealer? But I think that in context it would normally be clear.
You can say that a mechanical part is "free" meaning that it's movement is not restricted, usually used as the opposite of "jammed" or "stuck". Like, "The gear was caught on that loose spring, but now it is free." I can imagine a sentence where that would be ambiguous, like, "Hey, I see you got the lawn mower working again. Did you have to buy a new part?" "No, the gear is free now." Does the speaker mean that he didn't have to buy a new part because it was available at no cost? Or does he mean that the only problem was that something was stuck and now that it is not stuck the machine is working without having to replace any parts? But again, I had to work a little to make that sentence ambiguous. Usually the meaning would be clear from the wording of the sentence.
As I said, lots of words in English have multiple meanings, so when it's not clear which meaning is intended, either use a different word or add a few words to clarify. Sometimes people have one meaning in their minds and it doesn't occur to them that other meanings are possible, and so they write or say something that comes out unclear. Comedians often deliberately play on multiple meanings to make a joke, especially if one of those meanings has something to do with sex. But it's not necessary to add words when there is no ambiguity. Doing that just sounds strange. "Get a bar of soap free with every $10 purchase!" is completely clear. You don't need to explain that the soap is not politically free or able to exercise free movement, as neither of those makes sense in context anyway.