How to determine if an area defined as a "way" is part of a geographical location?

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1

This is the “way” location I’m referencing:

In checking several non-authoritative sources (e.g. Google Maps), I’m finding that this section of town resides in Bee Cave, TX

The geographical border of Bee Cave seems to wrap around this area (maybe previously undeveloped?):

What is the best process for determining where this section of town resides and having it added properly (or determining that it is added properly and should exist as defined)?

Thanks in advance and please feel free to correct any terminology that I may have misused.

2

According to the county GIS map:

It’s not part of any city, so “in the county” as we say in Kentucky.

According to this

The subdivision is named “Lake Pointe”