It's not terribly consistent, even within monolingual dictionaries. Whether two words are considered separate entries, or whether they are the same entry but use different kanji for different meanings, it's hard to predict how dictionaries will handle it. Your best bet is going to be to look at a Japanese resource for which kanji goes with which meaning.
It's an interesting question, and something I'd like to know more about. Trusty 大辞林 has three entries for 1) 暑い, 2) 熱い and 3) 厚い, 篤い. So what is あつい actually? 1 word with 3 different broad general meanings, or do we have here 3 words that just happen to share the same pronunciation? Or maybe that is all arbitrary to a certain extent.
When I was researching how the nomenclature works for English, I stumbled upon the nicely made info chart on this page: https://www.oxford-royale.co.uk/articles/efl-homophones.html
Well, I guess that all makes perfect sense, but it clearly doesn't make this any easier haha.
"Alternative Forms"
I am aware that sometimes to different words spelled differently can be read the same like 暑い (for hot climate) and 熱い (for hot people) but when Jisho says "Other forms" is that the same thing? I'm specifically talking about 上る's other form 登る.