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I am doing some cleanup of a GIS with a vast number of point feature classes, some 50,000 points in total. In addition, I have a polygon feature class that divides the project area into distinct districts.

The point features all have an attribute (DISTRICT) that is intended to identify the district in which they lay, and this is supposed to correspond directly to the district name attribute (DISTRICT_NUM) in the district polygon feature class.

However, this DISTRICT attribute has many null or incorrect values, and will have to be redone in it's entirety.

What tool or combination of tools could I use to automatically fill the DISTRICT attribute in the point feature classes based upon the DISTRICT_NUM attribute of the polygon those features lie entirely within?

Some limitations: I don't have any way of adding new feature classes to the overall GIS, so processes that create new output feature classes will not work. Nor can I add additional fields to either feature class. That aside I have every license level and nearly every extension for the ArcGIS Pro application of ArcGIS Desktop.

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Sounds like a Spatial Join would do the job. From the documentation:

Joins attributes from one feature to another based on the spatial relationship. The target features and the joined attributes from the join features are written to the output feature class.

I assume you just want to keep DISTRICT_NUM and not all the attributes from your Polygon layer. In this case, the Field mapping parameter would be useful:

Controls what attribute fields will be in the output feature class. The initial list contains all the fields from both the target features and the join features. Fields can be added, deleted, renamed, or have their properties changed. The selected fields from the target features are transferred as is, but selected fields from the join features can be aggregated by a merge rule. For details on field mapping, see Using the field mapping control and Mapping input fields to output fields. Multiple fields and statistic combination may be specified.

This way, you can specify that your output feature class contains just the DISTRICT_NUM attribute and even rename this field.

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You can use the Identity tool to populate a new attribute field in a new point feature class with the unique identifier of the polygon each point falls within.

This tool requires an Advanced level license.

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