Are you thinking a tender offer somehow overcomes the poison pill?

Yes, if he launches a tender the offer goes to the shareholders. He wouldn’t need to build a larger stake himself.

A tender offer is a means of building a large stake, so the poison pill would still be active. Therefore, he will not launch a tender offer.

I hesitate to speculate on what Musk will do specifically, but often in a poison pill situation a tender offer will be contingent on the removal of the poison pill. The point of the tender offer is not to buy the shares immediately, but to incentivize shareholders to put pressure on the board to remove the poison pill, then complete the tender offer it's removed.

Incorrect.

I don’t think this is correct.

It is correct. That is how a tender offer works.

From Matt Levine:

"Musk can launch a tender offer to buy all of Twitter's stock for $54.20 in cash. (Or, of course, some higher number.) The tender offer is a public, binding document filed with the SEC, open to all shareholders, and it will be full of disclosures about his plans and, in particular, his financing. Shareholders will be able to read it and see if he has the money. If it looks like he does, then they will be able to decide if $54.20 is a good enough price. If they think it is, they will be able to tender into his offer, submitting their shares for purchase. He won’t be able to buy them, though, because of the poison pill; the tender offer will be contingent on getting rid of the pill. But if like 90% of shareholders tender into his offer, then that is an important public-relations victory; he can go to the board and say “your shareholders want this deal, let them take it.” And then the board might agree and get rid of the pill, and then the tender offer can close and he can buy the shares."