Does the rule apply to all shareholders? I don't really see how a publically traded company can put an arbitrary condition on what can be done like that - any borrowing can be a totally private deal between you and a bank (or another private individual) - Tesla isn't even privvy to such deals, so how can they enforce any rules about them?

Large shareholders have different rules and restrictions. For example, you can go buy TWTR all you want, but Musk had to report when he had obtained a certain percentage.

Remember that Musk is not only a shareholder of TSLA, but also an employee.

Tesla is not the lender, Musk's broker is.

Therefore Tesla has zero input into margin rate broker decides to give Musk.

No, Musk has an agreement with tesla that he can only borrow against a quarter of his shares. He's already borrowed against quite a few too. Musk could go to the board to get that number bumped up, but until then he can't just borrow the full $21 billion against his shares.