How can I organize hobby supplies that come in many tiny parts?

Use a portable multipurpose organizer with multiple compartments and a handle. Give each type of small part its own section, label the sections if needed, and keep the entire organizer together so you can take it to your work area and put it away easily.

Start with what you already own and how often you use it. Edit first, then choose a home for each category and buy additional storage only if there is a genuine gap.

My final check is practical: can you find what you need quickly, put it back just as easily, and see when the space is getting full? If not, simplify the categories or move the storage closer to where you use it. An organizing system should make life easier, not become another chore.