As the comments for the question mention and to provide an answer for this question. You can use the "specify a minimum feature size" via the Maplex Label Engine approach which can satisfy the spacing that you are looking for when viewing/placing labels in ArcGIS Pro.
A way to control label density in an area is to reduce the number of small features that are being labeled. If your layer contains many small insignificant features that do not require a label, you can use the Maplex Label Engine to remove the features from the list of features to be labeled.
The Minimum feature size property is only available for line and polygon features. For line labeling, the value is specified as the length of the line in the current map units or in page units—millimeters, inches, or points. For polygon labeling, the value is specified as the length of the polygon perimeter or the area in map units or in page units—millimeters, inches, or points.
Specify a minimum feature size for labeling
Ensure the Maplex Label Engine is enabled.
Ensure Labeling is the active way of displaying the Contents pane.
Select a label class in the Contents pane and click the Labeling tab.
On the Labeling tab, in the Label Placement group, click Label Placement Properties Launcher.
On the Labeling pane, click Position and click Conflict resolution.
Expand Minimum feature size.
Specify the Minimum for labeling size and the units to measure in (map units or page units—millimeters, inches, or points).
When labeling polygon features, specify whether minimum feature size is for Perimeter or Area.