I figured out how to switch it to email codes instead of texting them. On the website, open the Settings page, then under Phone Numbers click "Change" next to your mobile number, uncheck the box next to "Send you text messages", and click "Done". Or, in the app, tap your profile icon in the top right, then tap "Account info", then "Phone Numbers", then your mobile number, and turn off the toggle next to "Send you text messages". Still no way to disable the feature entirely, unfortunately, but I trust my email account's security a lot more than I do my SIM card's.
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