There's no edit button on Mastodon (partly due to the massive potential for abuse), but there is something similar called "Delete & re-draft".

Selecting this option deletes your post and puts it back in the editing box so you can quickly make changes and re-post it. Note that this will orphan any replies and remove any boosts or likes.

You can do this by clicking "..." below one of your posts and selecting "Delete & re-draft".

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