So for an institutional investor, a negative yield bond is essentially a hedge against bank failure?

Also, look at it this way, if you have, let's say $5b on deposit at a bank, and you need to give it to someone else for some reason. Well transferring that money could destabilize the bank. They might refuse to let you withdraw it quickly. etc.

Bonds are easily and instantly transferable privately without causing major market loss.

This is the thing about huge finance like this, there's a gravity to money, and your intuitions from having bank accounts, money, etc, doesn't apply because entirely new problem appear you will never have. What if every time you paid a major bill at your credit union you threatened the solvency of that institution?

Yea that’s a good way to think about it

Does that mean a negative yield indicates a loss of trust in banks? That institutional investors are so desperate to avoid relying on banks that they're willing to take a loss on gov't bonds?

No, institutional investors never put vast sums of money in banks, regardless of the yield.