Incorrect information about free space on internal Macintosh HD

Modern macOS file systems are very complicated. The parent/child relationship you think you see is backwards, kind of. It is a challenge to even explain it. Files can exist on multiple places on the disk, but take up space only once. The operating system freely mixes up actual "free" storage with "used" storage that could be made "available" at some point, if the operating system (not you) decided that it needed it.

I can tell you that what you see in Disk Utility is correct. That is one of the few, relatively truthful displays. What it says for "available storage" is actually your free disk space. Anywhere else in the operating system that says "available" storage is simply a lie.

And yes, local snapshot can be a big part of that.

There are a lot of local Time Machine snapshots. That could be taking up space. Time Machine will make local snapshots if there isn't a backup drive connected. Local Snapshots should be removed if space is needed. They will eventually be culled into a regular backup.

You can manually remove them use this command in Terminal:

tmutil deletelocalsnapshots /

The header you have selected in the disk list is a grouping of everything that makes up the Startup drive.

The OS takes up ~16GB.

The Data volume takes up most of the rest. There are a couple other hidden volumes, Preboot, VM, Recovery, Update which you see in your Finder list.

The Macintosh HD volume you see in Finder is a synthesis of the same things.

All of those under Volumes are synthesized mount points for the parts of the OS. The top-most folder, System, doesn't show what is in those mounted volumes as they are just mount points for the file system to access the data on the actual volumes.

Trying to make sense of the way Big Sur and later organize the parts of the OS is much like trying to read the output of the Console app. You will end up driving yourself crazy trying to make any sense of it.