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Kind of hard to tell due to this seemingly being the least photographed case in the universe, but might the G-Alantic GA-3102 suit your needs? The design is distinctly late 2000s/early 2010s, but it does seem to be a slim/flat mATX case at least. As for using an external PSU, you'd need an internal DC-ATX unit like J-Hack's One2, GuryHwa's G-Unique ArchDaemon or the classic PicoPSU for a 12V system, or something like a HDPlex for a 19V one, plus a suitable power brick of your choice. There are cheapo units to be found on AliExpress/Ebay too, but their quality is dubious. For a system with a 65W CPU, a single drive and a couple of sticks of memory you'd need a >100W unit (dependent on how closely CPU power draw adheres to TDP - some CPUs can draw a lot more while boosting).