UPDATE
My question relies on the result of compiling the test project I made (which I linked below), which clearly indicates that the fonts are not being found. While having the fontawesome5 package as part of the TeX distribution used by Overleaf is customer-service related, having this particular problem I described here is not. This could happen apart from Overleaf. For instance, if I wanted to use a custom-made package with included fonts, or a CTAN zip of the same sort, in a local, per-project fashion, without installing it to the computer. That's why I consider this question important and not eligible for closing.
Furthermore, I admit the phrase "I don't think they would respond. Look, if they would, the package would've been added ages ago!" was totally unfair for the Overleaf team, who have made an excellent work. So I apologize publicly here for those words I said.
UPDATE #2
Unless people with more knowledge and experience about using this website decide other options, and considering the question was indeed answered, I'll leave this question as it is for the record, to show other users and myself how to and how not to interact with others here.
I tried the procedure described in the answer of this question on Overleaf v2 (as the fontawesome5 package is still missing in there) to no avail.
The small document I made to test this is available here (read only).
Let me note though, that the only difference between that question and this one, is I'm using XeLaTeX.
In particular, the two errors related to the package are:
Error #1.- /fontawesome5/tex/fontawesome5-utex-helper.sty, line 59
Font TU/fontawesomefree/solid/n/12=[FontAwesome5Free-Solid-900.otf]:script=latn; at 12.0pt not loadable: Metric (TFM) file or installed font not found.
<to be read again>
relax
l.59 ...ze_font:nn{\c__fontawesome_kind_tl}{solid}
I wasn't able to read the size data for this font,
so I will ignore the font specification.
[Wizards can fix TFM files using TFtoPL/PLtoTF.]
You might try inserting a different font spec;
e.g., type `I\font<same font id>=<substitute font name>'.
Error #2.- /fontawesome5/tex/fontawesome5-utex-helper.sty, line 60
Font TU/fontawesomebrands/regular/n/12=[FontAwesome5Brands-Regular-400.otf]:script=latn; at 12.0pt not loadable: Metric (TFM) file or installed font not found.
<to be read again>
relax
l.60 ...ntawesome_analyze_font:nn{brands}{regular}
I wasn't able to read the size data for this font,
so I will ignore the font specification.
[Wizards can fix TFM files using TFtoPL/PLtoTF.]
You might try inserting a different font spec;
e.g., type `I\font<same font id>=<substitute font name>'.
And then, I'm unable to use the package at all, because commands like \faCircle aren't recognized.
I'm pretty sure I'm missing something for this particular configuration. What would it be?
What do I need to do to make this package work on Overleaf when using XeLaTeX?
CS-like questions are off-topic in this site. Since, this question falls under the scope of one such, I voted to close. However, there are some overleaf questions, in which it is aTeXrelated issues and such a class of questions are on-topic in this site, I think. – Raaja_is_at_topanswers.xyz Mar 16 '19 at 06:20;). However, if you expect us to help, please provide us with a MWE that clearly reproduces the issue in hand. – Raaja_is_at_topanswers.xyz Mar 16 '19 at 07:14