EDIT:
The root cause of the error is likely that you have a reference to Microsoft DLL in your Acumatica DLL extension project.

And you also likely have a Website in the same solution which adds the extension projection reference. To check this, right click Website go to Property Pages and check in References, with Add Reference button in Project reference section.

This setup copies references automatically when you compile. You can remove copying of some references with CopyLocal=False property. However this doesn't appear to apply for Microsoft.Bcl.AsynInterfaces. Maybe you used Bind feature in Acumatica Customization page to set-up that automatic copying or created the extension C# project from the Acumatica Customization page.
In case the website is broken by a DLL file in Acumatica Bin directory. To restore original DLL files use Acumatica ERP Wizard (same version as corrupted website) and select 'Perform Application Maintenance'

Then select the corrupted site and run 'Update Only Website':

Check the date of the DLL which was previously corrupted:

Then identify the process which replaces the original DLL file shipped with Acumatica by a incompatible version and remove it. I suspect you are compiling a C# project in Visual Studio. And this project is configured to deploy files directly into Acumatica Bin directory. After compilation the date of the corrupted DLL file would change in Acumatica Bin folder.
Try removing the website from your solution if it's there and has a reference to your C# Acumatica extension project:

If there's a Post Build script (project properties-> build) that replace Acumatica DLL remove it.
Then compile to any directory that isn't Acumatica Bin folder. This is configured in C# project properties build section.

After compilation copy only the required compiled files which does not include 'Microsoft.Bcl.AsyncInterfaces.dll' to Acumatica Bin folder.
This copy operation can be done manually, with a batch file, with a post build script etc... The important thing is that it shouldn't copy DLL files which are already shipped with Acumatica.
One other possible solution is to select the same .Net Framework version that the Acumatica site uses in your own extension DLL. That way when compiling you would be replacing Microsoft DLL with the same version.