Do my brands need their own statuses to send brand-specific communication to consumers?

No. Let's say you have Brand A and Brand B and you want both of them to use a status called "Hot - Day 1" to send a text message to consumer. You can use the same status for both brands regardless of who owns/created the status. You do NOT need to create a separate "Hot - Day 1" status for each brand.

Here's why that works. Statuses are applied to a consumer or policy regardless of brand. For example, a status that includes a task to send a text message including the marketing variable of {{}} would fire with the name of the brand that consumer is assigned to regardless of who owns the status that fired that task. The ownership of the status as well as the “visibility” (global, user, or user and descendants) is what dictates/allows a status to be seen and then applied/used with a consumer. It does not control the branding applied to a consumer.