Employment has fallen slightly recently: https://fred.stlouisfed.org/series/CE16OV

Not dramatically though, a more charitable view would say that employement levels are fairly flat.

The unemployment rate is also extremely low by historical standards, even when taking into account the various measures of unemployment. There is also plenty of evidence that businesses are finding it unusually difficult to hire employees. The Fed is probably fine with the unemployment rate rising pretty significantly because they probably don't see the current rate as being sustainable.

> The Fed has no mandate to generate or maintain economic growth.

Correct. And yet they let inflation get this bad, so it seems like they're trying to avoid recessions even though they haven't been told to.

Or they believed it would be transitory and any action would upset longer term price and employment stability.

You don't need to guess; you can go read the minutes of prior Fed meetings here:

https://www.federalreserve.gov/monetarypolicy/fomccalendars....