Badge description (like "You added a co-maintainer to a package. BFF!"):

Awarded to Mentors and Students participating in Summer Coding activities like Gsoc,Outreachy(summer,winter).

1) What are those activities?

Those are mentoring/internship programs where someone from fedora is the mentor to students participating in gsoc or outreachy. Mentees learn to build software or design practices through the summer/winter of these programs.

2) Who is doing them (are they packagers? translators? newcomers? veterans?
users? sponsors?)
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NewComers,Veterans,Packagers basically a varied lot.

3) Why are they doing them (is this a means to a different end?)

same as question 1

4) When do they do them (every day? once a year?)

Gsoc in Summer and Outreachy in summer and winter twice a year.

5) How do they do them (by talking in IRC? by running commands in the console?
by using a web interface?)
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IRC,Web,Bluejeans,Zoom,Telegram and similar communication platforms.

Lastly, do you have any ideas for artwork concepts?

So basically the current summer coding badge are a pair of socks. Originally they were design to represent soc in Gsoc the short form of Google summer of code. Fedora has come a long way from then,having expanded into outreachy which runs twice once in summer and once in winter.
Also socks just dont speak of mentoring or even summer,summer should be blue skies,sun,flowers and such stuff.

So i suggest either something that represents mentoring along with ascetics of summer like sun,blue skies etc shoule be done in the badge or replace the badge with a more inclusive mentored program badge that represents gsoc,outreachy(both summer and winter).