Is there a function that can be called to sharpen images in EO Browser?
No, there is no such thing.
Sentinel-1 does not have a “sharpening band” (similarly as Landsat-8 has), so this is not a straightforward thing to do. You would need to use some sort of machine learning, e.g. like this one (but with SAR data):
https://mdl4eo.irstea.fr/2019/03/29/enhancement-of-sentinel-2-images-at-1-5m/