How much does a new battery for iPhone 11 really cost?

For what it'worth........

It's $89 (U.S.) in Apple's Support document........iPhone Battery ReplacementApple SupportOfficial Apple Support › iphone › repair › battery-re........but I was informed at an authorized service shop that the support document was out of date and the price would be $99 plus tax, so $106 and change.

$89 in the US. It may be different if you get it replaced outside of the US.

iPhone Battery Replacement - Apple Support