Need a virtual PBX type client-ATS-performer. Which one to choose (or write yourself)?

Question

VoIP

In more detail, the task is as follows:
There is an application in which a person wants to sign up by phone for some kind of paid service.
There is a phone number of a person who is on the phone, there is a database of those whose services can be ordered by phone (each has its own phone, and they are not connected in any way)
From a software point of view, it looks like this:

• By clicking on "Call", the application sends a request via API to us with CLIENT_NUMBER and CONTRACTOR where he calls, then we send it to the PBX
  
• Dialing to the general number of OUR COMPANY begins immediately
  
• The PBX receives the call, looks from which number it comes from and compares this number with the CLIENT_NUMBER in the applications. This is how the required application and the service they want to call are found.
  
• The PBX connects the caller to the appropriate service
  
• Call is being recorded, audio recording is available
  
• If the service does not respond, then the call is simply reset by timeout. If busy, it is also reset. At the same time, the usual generally accepted signals (short beeps or an answering machine message) are simply sent to the client's handset. The status of the dropped call is recorded.
  

Total:
we solved the issue through Asterisk. We found a person who set up everything we needed

Answer 1

Apparently you want a CRM system. But why invent everything "on the knee" if you can read and choose?
If we limit ourselves to PBX, then any IP PBX solves your issue.

Answer 2

Take the virtual PBX from WestCall (westvirt.ru) as an example, I have not yet come across a more thoughtful and functional PBX.

Answer 3

Yumajik has a ready-made solution, I can’t say with 100% certainty about integration with CRM, but I don’t think it’s a problem.