What are the mechanics by which they are going extend or extinguish the fediverse and how would they do that from a technical standpoint?

"Extend" typically means adding proprietary features to your own product that are incompatible with your competitor's product. For example, what if they added Gold (as in the old Reddit kind, not the current Reddit kind)? That obviously wouldn't work with Lemmy, or at least not right away. The Lemmy devs would have to try to play catch-up whenever Threads launched a new feature. And not every would be able to be made compatible with Lemmy in some way.

Second, why when the entire fediverse with years of time behind it is a rounding error compared to a product they launched like 6 months ago. Why does Meta give a tiny shit about the fedi compared to TikTok, for example?

There are several potential reasons for this. They could see Lemmy as a potential future threat, and using the EEE method may squash the potential threat before it actually becomes one.

ActivityPub itself is also actually a neat feature to offer. It's basically Single Sign-On (aka SSO) without a few steps. (This is not me giving Facebook the benefit of the doubt. Companies can have multiple reasons for doing something, and I cannot believe this is the only reason Facebook would experiment with ActivityPub.)

As for your point about TikTok, TikTok itself is already too big to use the EEE method. (It usually only works on smaller competitors.) Facebook is using a different method for that: it cloned TikTok. Their version is called Reels.

As for the "rounding error" comment, Facebook actually had "accounts" created on Threads for all of its Instagram users, so, while there may be billions of accounts, not all of them are active. As a matter of fact, I've heard Threads use dropped pretty significantly after its initial launch. In that case, Facebook could be using a strategy I've seen both Sony and Microsoft use in regards to their game consoles: whenever Sony is in "second place" in the its console war with Microsoft and losing users to them, it tries to get people to migrate back over by adding features its userbase wants. Whenever Sony is on top, however, they tend to stop listening to customer feedback and sit on their laurels. I've seen Microsoft employ a similar strategy, too.