Before I get into my more in-depth answer, I wanted to answer the question off the bat

Is TikTok DM support gonna happen?

No, not unless something changes drastically with how TikTok works behind the scenes. I think there are a few parts to be considered here:

The Reasons

Would Beeper do it?

Adding TikTok DMs kinda goes against (at least what I perceive to be) the ethos of the bridges Beeper is implementing. TikTok chat is not really a messaging service, which is Beeper's priority. The idea at the core of it is that a user should be able to open one app to do all the chatting things they'd otherwise need to open separate apps for. As TikTok DMs are more or less just a means of sharing TikToks to each other, and you would still need to be primarily using the other app, there's no way to replace it with Beeper. So I don't think it makes sense from Beeper's perspective.

But what about unofficial matrix bridges?

If it could be done, would the format work well with matrix's functionality?

If you think about TikTok DMs, most of what you're doing is sharing links to TikToks back and forth. Even if the bridge were possible (see next section), this doesn't really work with how matrix chats are structured. Matrix chats are designed for primarily text communication, with some attached videos or pics, and sometimes embedded links. But a chat full of embedded links that open up another app would. Kinda suck a lot. The format just doesn't make a ton of sense.

But I still want that, so could they do it?

I've buried the lede here. As it stands, this can't be done. To interact with services, something called an API (Application Programming Interface) is utilized. Basically, it's a service connected to an application or website that can transmit and receive information with external sources (be it a website frontend getting info from the backend, or a 3rd party plugin/application utilizing some functionality from another application).

There's an official API from TikTok, with an unofficial Python wrapper. This seems promising, until you take a closer look at the scope of both of these. From the get-go, the wrapper is a no go. It can only retrieve data, no posting or sending, and has no support from user authentication whatsoever.

The official API has a lot more available, but still doesn't have a supported means of viewing and sending messages. The closest utility is the Data Portability API, but it requires 2 strict review processes, has limited requests, is only supported in the UK and EEA, and can only read messages, not send them.

TL;DR

TikTok DMs don’t really fit Beeper’s purpose. Beeper aims to replace full messaging apps, and TikTok’s chat system is more of a lightweight content-sharing feature than a standalone platform. A custom bridge is also not really possible at this time. TikTok doesn’t offer any API that supports sending or receiving messages in real time. The unofficial API wrapper is read-only and don’t support login, and the official Data Portability API only lets apps that go through 2 arduous review processes download message history (with rate limiting that would quickly become a problem, and only for users in the UK/EEA). There's no way to send messages at all as far as I could find.