Hi there!
I’m a regular reader of this fantastic site but this is the first time I’m answering a question… because… I think it’s an interesting puzzler (and some might know I love to play ^^)
So… Indesign does not allow to use different formatting for footnotes.
You probably should forget about prefix and suffix and maybe think different.
I suggest you start by inserting 2 footnotes and then add manually round brackets before and after footnote 1 and square brackets around footnote 2. Then, select your footnote text number (at the bottom of the article) and do the same thing. Think character style in order to format brackets as superscript if you want. It can be on the pasteboard like in my example (see link)
Do not get scared… You’re not going to manually change the whole document that way ^^ Just the two first footnotes.
Then… All you have to do if you want to insert a new footnote is to copy footnote 1 or footnote 2, along with brackets and paste wherever you want to insert your new footnote reference.
See magic happen at the bottom of the article: the brackets appear…
If you want to change the brackets of a footnote, it’s a bit tricky because if you just replace the footnote, you’ll loose your text. So you should first copy/paste the right footnote reference. Copy/paste text and then delete the old one.
See the trick in action here: https://ibb.co/nphOEb
Now, I’m pretty sure crazy scripters could pop up an easier way, but since they haven’t replied yet, you might find this helpful.
Vinny