Yaarel
🇮🇱 🇺🇦 He-Mage
The rules-as-written include any backgrounds that the DM decides on.Those aren't rules for creating custom backgrounds. Those are rules explaining how to apply what's written in a background description to a character you're creating, plus a statement saying a DM might provide you with more background options.
Compare that to the "Customizing a Background" section in the 2014 Player's Handbook: "To customize a background, you can replace one feature with any other one, choose any two skills, and choose a total of two tool proficiencies or languages from the sample backgrounds."
Read that part about tool proficiencies again. Now consult the 2024 PHB and tell me: What tool proficiencies are you allowed to pick from when creating a custom background? Does the restriction from the 2014 PHB still apply? You can't actually answer that without seeing the 2024 DMG.
This means the same thing as "you and your DM agree on".
The rules are in black-and-white. I find it difficult to understand what you need the rules to say.
There rules are there. The DM is responsible for adding more backgrounds. The DM can add whatever backgrounds the DM wants. The DM can add a Freeform Background if the DM so decides.
The whole point is, the player doesnt get to invent a background without DM approval. So, if there is a certain background that a player wants, the DM needs to ok it. That is what the rules say.