Specifically, I’m aiming to have all points appear in solid gray when the map is zoomed out. However, when zoomed in, I want these points to display different colors based on a the word found in an attribute field.
If you can't find a "proper" way to do this you can always use the work-around of adding the layer to your map twice, set the symbology and visibility scale of the solid gray to "disappear" at the same scale you want the varied colors to appear. May not be as clean as you're hoping for when it comes to the legend or layers button but it will accomplish the task.
Though, this documentation explains how to show alternate symbols at different scales in Pro: Use scale-based symbol classes—ArcGIS Pro | Documentation
I think with some Arcade you could probably accomplish this?
Visualization | ArcGIS Arcade | ArcGIS Developers -- Check out $view.scale
I think you'd have to hardcode your colors, but basically if $view.scale >1:100,000 set the color to grey.
You can do this using Alternate Symbols.
Choose Unique Values
Click the Scale Tab
Select your symbol and then add alternate symbols to display at the specified scale.