I'm using some images (mainly as backgrounds, but otherwise I may as well) for my a website I'm making.
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No. Your website can be considered a 'medium through which you share the image', so you can use and share the image, while not sharing your own code.
But you DO have to share the image, and share any modifications you make to it. So if you're using a forest photo and stylize it or draw creatures in, you MUST allow other to use that image. And of course, you have to include proper attribution, so it'll affect your design/layout/sitemap a bit.
Collection vs derived work
TL;DR: my gut feeling is that it would be fine if you attribute the images on the caption, but I haven't found absolute confirmation, but the distinction between collection and derived work might be worth looking into
https://academia.stackexchange.com/questions/48375/using-images-with-cc-by-sa-license-in-slides-or-a-thesis/48382#48382 is for the image in book/thesis, which I believe is analogous for the game case.
In CC By-SA 3.0, there was clear distinction between "derived" and "collective" work, and it was explicitly mentioned that if you include an image in a book, the book is a "collective work", not derived, and does not need to be CC By-SA. So the image in game might be analogous.
"Collection" means a collection of literary or artistic works, such as encyclopedias and anthologies, or performances, phonograms or broadcasts, or other works or subject matter other than works listed in Section 1(f) below, which, by reason of the selection and arrangement of their contents, constitute intellectual creations, in which the Work is included in its entirety in unmodified form along with one or more other contributions, each constituting separate and independent works in themselves, which together are assembled into a collective whole. A work that constitutes a Collection will not be considered an Adaptation (as defined below) for the purposes of this License.
This was somewhat tested in US court for an Atlas at Drauglis v. Kappa Map Group, LLC where a 2.0 image was used as a cover of an Atlas, with attribution on the back cover, and no infringement was found.
However, it is hard for me to be sure if the "a single image in book/sofwtare case" is actually a collection or not. Can a collection have a single item? Are the icons of your UI a collection? Intuitively it does not feel like it, since their main goal is not to showcase the items, but rather to integrate into your work.
Also, in the case of a background website image, it does slightly further blur the line between derived and collected in my opinion, as it starts to feel more integrated into the website itself than a collection. But my gut feeling is that as long as you attribute it on every page somehow, it would be OK.
In 4.0 the term "collective work" was dropped, and things became even less clear, although most people are guessing that hasn't changed, although I could not find clear evidence. https://opensource.stackexchange.com/questions/7022/using-cc-by-sa-music-in-a-podcast/7036#7036 suggests that this distinction in 4.0 is simply delegated to your local law, or in other words, as a lawyer, and kind of reduces the usefulness of a license in the first place. The collective work wiki page has comments on it for several countries.