I came across a complete Malay version last year on a site called BacaNulis, though I'm not sure if it's still up. The text was surprisingly clean, with minimal formatting errors, which isn't always the case for older texts. You'll want to search in Malay; using the full title 'Hikayat Seribu Satu Malam' might get you closer to the original collection rather than adaptations.
If you're open to reading in English, Project Gutenberg has the Richard Burton translation, and that's completely free and legal. The language is archaic, but the footnotes are an entire rabbit hole themselves. Honestly, the Burton version feels like reading two books at once—the stories and then his obsessive, often eyebrow-raising commentary.
For something more modern, some university digital libraries host translated excerpts as part of folklore studies, but those are usually PDFs and not always the most convenient for casual reading. I ended up bouncing between a few sources because I wanted to compare how certain tales were framed differently across translations.