Nic is quite correct. I believe the SDK uses a simple "threshold" greyscale conversion method, with no dithering, and supporting transparency which is good enough for prototyping/placeholders. Whilst I'd love to see greyscale/dithering options in the SDK, with graphics baked at compile-time, I do believe your graphics should be prepared as 1-bit outside of the game.
Anyway, I looked into 1-bit-conversion options in detail when Playdate was announced, here are my findings:
Photoshop
Has one greyscale and a few dithering options to get you 1-bit (Image > Mode > Greyscale & Bitmap). But they're not real-time, and awkward: ufo.psd.zip (11.2 KB)
Pixatool
Abandoned app. Strange, frustrating UI, but nice results and some good options: PixaTool by Kronbits
Acorn
Acorn also has a great filter system that can be stacked to get realtime preview of 1-bit conversion, but is limited in types of greyscale conversion and dithering. Here's a sample file: 1-bit Workflow.acorn.zip (89.2 KB)
Classic Macintosh
There are many amazing tools for this on Classic Macintosh (1-bit b/w for a long time, and for years after colour was introduced). Anyway, I have a System 7 Virtual Machine installed with a bunch of graphics apps that I use: DeBabelizer, GraphicConverter, Photoshop 3, SuperPaint, UltraPaint, etc.
See this post on my blog: https://blog.gingerbeardman.com/2021/04/24/macintosh-drawing-software-compared/
Android
Web
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Canvas Dither
Last year after announcement of Playdate I found some web code for Atkinson dithering (the standard Classic Mac approach) on GitHub by @ticky (hi, thanks again, and great to see you on here!). I expanded on it a great deal - adding multiple dithering modes and greyscale options that I researched and implemented myself. Here is a usable version: https://www.gingerbeardman.com/canvas-dither/ -
Dither Me This - Image Dithering Tool
Part of doodad.dev "tools for making the internet fast, accessible, expressive, and green."
https://doodad.dev/dither-me-this/ -
Dither it!
https://ditherit.com -
Dither Paint
https://beyondloom.com/tools/ditherpaint.html