How can I know my if footage is rec.709 or not right out of the camera?
Knowing the details about what format your camera recorded is often as simple as consulting the manual.  However, some cameras shoot multiple formats, and often, editors are given footage from unknown or unreliable sources.  One of the best tools for discovering the full details of an A/V file is the command line utility, mediainfo.
Depending on whether or not your computer comes pre-installed with mediainfo, obtaining your answer may be as simple as opening the command line interface, and typing:
mediainfo /PATH/TO/YOUR/FIlE

If this returns a &quot;command not found&quot; error, then you will need to install mediainfo according to your operating system requirements.  On MacOs, the easiest way to install is through https://brew.sh
If the command line isn't your thing, there are GUI-wrapped versions available in both the Microstoft Store, and Apple App Store, caveat emptor.
The default output is the total information known to the operating system about the media file, which may be overwhelming.  Theres a good explanation of how you can return only relevant information here.
For example, to return only the colorspace, you would type:
mediainfo --Output=&quot;Video;%ColorSpace%&quot; /PATH/TO/YOUR/FILE

It's important to mention though, that not all metadata is created equally.  Different camera manufacturers will include different details, and when video files get transcoded, the metadata is often altered.
However, mediainfo is one of the most comprehensive tools available for discovering these sorts of details about a media file.