The best option to dispose of silicone and its chemical components is the local waste system. So first you should wipe the objects (containers and mixing instruments) with paper towels or old newspaper to remove as much silicone as possible. These should be disposed in the usual household waste, not in the recycling system. Just keep in mind that they stick to the waste container.
The waste is usually either burned (where silicone does not release any hazardous chemicals and releases less CO2 than plastics) or stored in landfills (where it takes decades to decompose but doesn't release any hazardous chemicals or micro-plastics).
What residue is left can be washed away with soap and water. Silicone is hydrophobic, so water cannot mix with it, but it's lipophilic, so it can be dissolved with soap or alcohol. All safety data sheets I found (links below) say to wash the silicone components away with soap and water and none of them indicate any environmental hazards. However, I assume you can clog up a drain pipe quite quickly when trying to wash away big globs of uncured silicone.
There are some studies that indicate that some chemicals released from silicone can cause cancer or infertility, so I would avoid releasing silicone components into the environment as much as possible.
I would also advice against any scouring agent because it only scratches the surface of the instruments but does no better than paper towels for the actual cleaning.
Here are some examples of safety data sheets of different 2-part molding silicone products by different manufacturers. (I'm not affiliated with any of them) You can read in all of them that the components are non-toxic and are supposed to be washed away with soap and water.