This was the first time Russia had deployed military police abroad. The experiment was clearly considered a success, and Moscow is now deploying battalion-strength scratch military police units created from several constituent elements but with no particular ethnic identity. By July, four battalions were operating in Syria, for a total of almost 1,200 effectives. Their primary missions are providing security for Russian facilities and personnel, and manning checkpoints and observation stations monitoring the “de-escalation zones” being established in line with an agreement reached in Kazakhstan in May between Russia, Iran, and Turkey.
There is no reason to argue that they are some type of new "robust soft power." Military police are good for counter-insurgency or peacekeeping type work because they are basically good light infantry.
Back in the 1990s, when some argued that in the post-Cold War end-of-history world America should convert Army combat units to constabulary units designed for peacekeeping missions, I argued in a letter to Army magazine that if we wanted that peacekeeping capability we should create more Military Police units that could fight or provide peacekeepers in line with rear area security forces. Constabulary units would be useless as combat units, I believed. (See my constabulary unit letter located here.)
Those military police units are Russian combat units. There's nothing soft about their power.