Is iPhone 16 waterproof?

It is not waterproof. It is water and splash resistant. You should not submerge it or put it under running water.

It should be able to deal with a splash here and there, but don't push it.

No, not waterproof. Water resistant to a certain degree.

click here ➜ About splash, water, and dust resistance of iPhone 7 and later - Apple Support

No. No iPhone or about any other electronics have ever been waterproof. Some such as iPhones are considered water resistant, but that was done with pure water in perfect laboratory conditions, where it does not really mimic real world conditions your iPhone can face. If it was just a little water, it should be okay.