On the plus side, Tineye can be quite helpful for finding things in their original size.
And I only use 1080p!
Use the HST and JWST pages for space wallpaper sources[1][2]. Make sure to check only the 'observation' checkbox; this filters out all the infographics, 'artist's impressions', simulations, etc.
I suggest downloading the TIFF, opening this in some photo post-processing program (Lightroom, Darktable, RawTherapee, etc), and applying mild tone and colour adjustments, and then cropping to the exact resolution of your display.
I get much better results this way.
My favorite source for all space-related pictures are the Apollo flight journal photography archives[1].
I’m not sure if there’s a better resource, as-is you have to click through to see a higher resolution version to check if the picture is even in focus, but honestly that adds to the fun of it :)
[1]: https://www.nasa.gov/history/afj/ap08fj/a08-photoindex.html