It doesn’t matter what the client is, the main question is: “Can you move the mouse cursor on your PC from anywhere without installing software”
The short answer is no, that's good! Otherwise, any user on your network can simply take control of your computer ...
Nevertheless, theoretically you could create an RDP ( Remote Desktop ) connection and use it to control the PC as a whole - but it is very difficult, already done and will still require the user to allow remote connections to the desktop with the computer (Control Panel- > System-> Advanced-> Remote)
Edit - Minimum minimum application:
There are several ways to approach this, but the absolute simplest application that I can imagine assumes that there is an application on the PC to listen for connections on the TCP / IP port. Then you send messages to this port with Android using the Sockets classes.
The application will receive these messages, analyze them and perform the appropriate mouse actions.
Make sure that you turn on the authentication / authorization mechanism - you do not want random strangers to be able to control your computer just because they violated your Wi-Fi.
It may be easier for you to create a desktop application for receiving messages using the HTTP protocol ( RFC ) - this is a standard, widely used and very flexible client-server interaction mechanism. Why reinvent the wheel? It will also simplify your code on the Android side, as you can use HttpURLConnection and other similar classes that abstract the complexity of socket management.
You might also consider whether the application should provide any feedback to the client - for example, a new mouse position or success / failure.
Note. Running the application as a Windows service or a website may seem preferable for a desktop application (it does not need to be launched by the user, nothing in the taskbar / system tray), but there are also big drawbacks - Windows services cannot easily intercept the desktop (what happens, if no one is registering?), and the websites work as another user, therefore, in addition to the fact that they do not have the same desktop, they have limited permissions.