@L4d1k thank you for messaging me your support case. I really enjoy trying to figure out the pain points and I think there is an explanation for the behavior you are experiencing.
I was able to get this to work via Systems Manager, and your setup for com.splashtop.Splashtop-Streamer may actually be working too. I believe you may be confused by the macOS System Preferences UI, which is not a good representation for the actual PPPC settings on macOS (let me explain this a bit).
First, here is the setting I used to successfully enable Accessibility for com.splashtop.Splashtop-Streamer:
"Accessibility" allows you to control the user's screen (control the mouse movement, specifically, with Splashtop). With this^ PPPC profile scoped to a macOS device who has com.splashtop.Splashtop-Streamer installed, I am able to control the user's screen without needing to have the end user enable "Accessibility" for "Splashtop Streamer" in System Preferences. However, if you look at the macOS System Preferences UI, you will notice the checkmark is still unchecked (this is normal!):
To further confirm the MDM PPPC profile is working: as soon as I remove the PPPC profile and restart the Splashtop app, I cannot control the user's screen anymore. Once I rescope the MDM PPPC profile again, I can control the screen's mouse movements again. This is working as designed, and the Systems Manager PPPC profile is actually enabling com.splashtop.Splashtop-Streamer, despite it being unchecked in macOS Systems Preferences.
Whats displayed on macOS 10.14 and 10.15 in System Preferences > Security & Privacy > Privacy are only the decisions end users made with prompts presented to them, not settings pushed via MDM profiles. Its essentially displaying the values that are stored in the TCC databases that can be found at /Library/Application Support/com.apple.TCC/TCC.db or ~/Library/Application Support/com.apple.TCC/TCC.db.
These are some of the quirks with PPPC via MDM on macOS Catalina right now, but it is the behavior all MDMs are facing. The Systems Manager profile is actually working to enable Accessibility for com.splashtop.Splashtop-Streamer, at least in my quick repro.
(Sidenote: if you have a test device, you may find it useful to reset all of the local PPPC settings before trying again with this command: tccutil reset All)
Can you confirm that if you use the same PPPC profile from Systems Manager (screenshot above) you are able to control mouse movements with Splashtop?