If the app, or web browser is not pasting text via Command-V (or via the app -> Edit -> Paste menu item, then it is an issue with the either the app or the Javascript running in the web browser.
I have not seen this kind of issue with a web browser interface, but I have seen it with some VNC implementation. Especially if the VNC viewer it connected to a Linux system, where middle-click is how you paste on the remote system. And since macOS does not have a middle click by default, you need 3rd party utilities to simulate a middle-click.
PS. You can get 3rd party Clipboard Managers for the Mac, but they focus on saving each Copied item, and allowing you to select which item you want to Paste. It does not have anything to do with sending a Paste to a remote system.
Also when using a VNC interface, the remote system needs to run something like vncconfig to map the remote clipboard to the VNC server.
Lots of moving parts when dealing with remote systems. And a lot depends on exactly how the remote viewer is operating.
NOTE: My Wife deals with VMware's vCenter on a regular bases via a web browser, and says she does not have any issues pasting. So I do not know what the issue is with your implementation.