Quote:- "Since my first language is not Chinese, for now at least I can't determine the best answer"
I think your problems are:
You are attempting a word for word translation of a complex sentence,
and seeking a singular definition of a single word in isolation, in this case “还”, that fits snugly into the complex sentence.
The word “还” in this sentence should not be read in isolation, because it contains multiple meanings / definitions some of which do not fit into the sentence in question, hence your "problem", and the many versions you find in the answers given.
In my view, the word “还” in the sentence is part of a compound phrase, namely, "还放回" All three words should be taken and read as a whole, that is, as a compound phrase.
You will encounter many such compound phrases in your studies, and you just have to get use to them, and eventually be able to recognize them when you see them. Takes time and lots of reading of course.
Thus "还放回" here simply means, in plain English, "return to" or "put back to", as simple as that. There is no need to hunt down every possible meanings / definitions of "还" and see which one fits, because without taking in the other two words, 放回, and read all three together as one compound phrase, you will be going round in circles, because of the multiple connotations attached to "还", and at your level bound to be understandably confused.
So, the material part of the sentence, 还放回原处, simply means, "return (them) to / put (them) back to their original places"
In conclusion, the word 还 in this context means "return", and since Chinese do not have "to", it needs 放回 to "complete" the "action" of returning.