If so, it would manifest as sabotage of satellite launches. There may, indeed, have been some of that down the years.

Most satellites are tracked outside of the controlling entities. See the various posts over the years tracking DARPA experimental long-term flight and return to earth vehicles. There have been some about Russian satellites having encounters with other satellites.

This is to say, if there was something significant going on, there's a very good chance it will be known.

It's more of a cold war because the assets are being put in place but they aren't being used in anger. There are satellites taking pictures of other satellites. There are anti-satellite missiles. Satellite capture/grappling mechanisms are being tested. We don't know what the X-37B is doing but it could capture small satellites and return them to Earth. Orbital drop pods and orbit-to-ground missiles are being developed. This is all unclassified so there could be more.