I need to create an App Password.
https://support.atlassian.com/bitbucket-cloud/docs/create-an-app-password/ says I need to click my avatar/profile image and choose "Settings" or "Personal Settings".
These do not exist in my Bitbucket UI. Where should I be looking? I crawled through every link in my Manage Account section.
So! It turns out that the Profile icon shown on Bitbucket.org is different from the profile icon on support.atlassian.com.
That makes the docs a bit misleading, as you're reading them while you're logged in with your Atlassian account, and they say to click Profile... and of course they mean, "Go over to Bitbucket.org and click Profile there."