Those are possible, but ugly solutions. Two cleaner ones are either depracate and remove the v1 api altogether, or when inserting a record to the database from the v1 api, use a default dummy value for avatar_url.
Although I agree with the comments above, adding a field is also a breaking change, even with a default value. Especially prone to this is any openApi client (speaking from experience ...). Maybe filtering it out would be an actual solution without breaking anything. An API update shouldn't need to update my implementation because it's not working anymore, in that case it's a breaking change and a major version bump.
