Were moons used to measure time IRL?

A simple question that’s been boggling my mind for years: Were moons ever used as a measurement of time in real life? If so, how long does one moon roughly equal to in modern-day time measurements?

We get the word “month” from an old word for “moon.” So when people use idioms like “many moons ago,” it is understood as “many months ago.”
 
A month corresponds roughly to one phase of the moon’s orbit. It’s not precise, partly because the Gregorian calendar that just about everyone uses is a solar calendar and is based on the Earth’s revolution around the Sun. That’s why we sometimes get events like a “blue moon,” two full moons within the same calendar month.
 
But some cultures - the Arabic world comes to mind - have historically used a lunar calendar, with months properly beginning and ending upon a full cycle of the moon. However, this makes their measurement of days in a year different from what we’re accustomed to to the point where someone may actually be a couple “years older” on the lunar system.

@DragonBoi471  
The Jewish calendar also still uses a Lunar calendar for months, and a Solar calendar for years.
 
Lots of real world calendars used a lunar cycle, but it doesn’t line up with the solar calendar so months kept slipping their positions in the agricultural/solar year.