Lasers have been used to shoot down satellites before, by both the US and China. Those shows were not really about satellites, they were about hitting long range targets moving at above “mach 10”.
The effectiveness of a laser system, is neither about speed nor range, but about exposure time of the target. They need more time than a high velocity explosive to disable a target, and they need it to stay in line of sight for that time… but once they get that, nothing can beat the speed of light.
Drones, are more likely to be able to hide until the last moment, but a strong enough beam may not need much time to disable one… yet any explosives attached, might still reach their target. Shells and mortars are a mixed bag, they may offer longer exposure, but not necessarily enough to get disabled before impact. Rockets can be turned into falling balls of scrap, but also become ballistic explosives. High maneuverability airplanes and missiles can be a serious challenge, particularly if they fly low enough to stay out of sight. Ships would make great targets, if it wasn’t that they’re massive heat sinks, and usually equipped with something capable of shooting back along the laser beam to wherever it’s coming from.
Where lasers outshine themselves, is at targets with low angular speeds, long line of sight times, following a predictable trajectory, which can’t shoot back. That includes trees, blimps, satellites… and ICBMs.
If Russia doesn’t have some serious lasers under the sleeve, and nothing indicates towards that, then MAD is broken and using Russia as an ICBM testing ground becomes viable, for at least the US and China.