I don'have the figma draw mode.

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I'm having the same problem... after I joined the Edu Plan, Figma Draw disappeared from the toolbar :(
I've tried closing, browsing, refreshing, and clearing cache/cookies, but nothing works.

Try this if the Draw tool is missing.
Click on your name or team name. A dropdown will appear select your team where the Education or Professional plan is active. Then create a new file from there. When the file is created inside the team, the Draw feature should appear in the toolbar.