Hi @Bud was that dataset derived by running a system geoprocessing tool or a custom ModelBuilder model or Python script tool? Has that dataset been used in a ModelBuilder model or Python script tool that applies the thick red line and labeling?
I am asking, because for a number of system geoprocessing tools and custom ModelBuilder or Python script tools that define the symbology of the output parameter, the geoprocessing framework stores a layer file representing that symbology and other layer properties in the dataset metadata so that if the dataset is added to another map, the symbology and layer properties are consistent to when the tool was originally run.
This system was put in place early in Pro 2.x. The goal was that the result of an analysis often has a specific symbology and layer properties that are necessary for the result to be interpreted and understood, and when that info was not stored with the dataset, only the layer produced by running the tool would have the full information necessary for the result to make sense. It's been several releases at least since the Geoprocessing framework has done this. I am not familiar with the thick red line with labeling, so that's why I'm asking about custom model or script tools.
A way to be sure the layer file has been stored in the dataset metadata is by exporting the metadata to an xml file and look for the LayerFile tag. Right click the dataset in Catalog and select View Metadata. In the Catalog ribbon tab, in the Metadata group, click Save As>Save As XML>All Content. Use the browse dialog to select a location and name for the xml file. The xml file will look something like below including the LayerFile tag (I highlighted in Purple - also the XML has been "pretty printed" for easier readability).

When this LayerFile is present in the dataset metadata, when the mapping system adds that dataset to a map, the LayerFile properties are automatically applied to the layer.
If you find the LayerFile and do not to keep this information, you can delete that part of the XML, save the file, then back in the Catalog, select the dataset, and in the Catalog ribbon tab, in the Metadata group, click Import and browse for the XML file that you saved with the cleaned out LayerFile.
If you can find what system or custom processes have been run using that dataset (the XML metadata also contains a useful lineage tag), we can then find out why the LayerFile had been embedded in the dataset metadata in the first place.