Consider the cover picture on this website - TortoiseGit
It looks so good, despite not having much detail and not even many colors. What tools/software might be used to create such graphics?
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Vector software is what would be recommended for that style of graphics (colloquially called flat). If you don't want to get a CC subscription just for Illustrator there are a lot of great options, including the newly launched Affinity Designer.
That style of graphic is also available to buy on sites like Creative Market or Graphic River, if you just need one to use on your site and aren't out to learn how to become an illustrator.