The words 'plus' and 'also' are not exactly interchangeable - by that I mean you cannot just swap them out in many contexts. For example, you could say "I'm a teacher, but I'm also a cab driver". You'd have to re-write the sentence considerably to use 'plus'.
If you look in Cambridge, you'll see one definition of 'plus' is "and also". The 'and' is significant. We say "and also" when something is additional, and it is this context where we can switch "and also" with 'plus'. For example, some people may count adults and children separately for specific purposes, and you might hear "there are 4 adults, plus 1 child". You could instead say "there are 4 adults and also 1 child".
I'm sure that in everyday speech there are some examples where 'also' and 'plus' are used in an interchangeable way. Very often someone will finish a sentence, but then begin a new sentence as an afterthought with either "plus..." or "also...". This is rather like beginning a sentence with "and", which some insist is wrong, but is common in extemporaneous speech and therefore often reflected in writing too.
I agree that other uses of 'plus' have "positive" connotations (eg "it's a real plus") but in the contexts where it means "and also", it doesn't really indicate anything positive, it's just a conjunction. It certainly isn't negative, but it introduces something that is probably an afterthought, or secondary to the main point you already made.