Choosing the right software is key to a smooth workflow. My go-to setup for the initial drawing phase is Affinity Designer 2 on the iPad, which offers incredible precision with the Apple Pencil. But don't worry if you're on a budget—Inkscape (along with the Ink/Stitch plugin) is a fantastic, open-source way to bring your embroidery designs to life.
You can use any vector- or digital drawing software as Krita, Procreate, adobe Illustrator, Canvas, Adobe Photoshop, Corel draw etc. as you want.
After the design fase, you can just import the embroidery design to Inkskaoe/Inkstitch to give it embroidery properties and export it to the right file format.
You can even code your design.