Sounds a lot like malware infection. 🙄
That is more evidenced by when you restart your PC, it doesn't instantly do it, but starts doing it after some time (when malware activates).
Since if the issue would be with the mouse, you'd get same issue even in BIOS/Windows log-in screen.
Also, mice, on their own, have 0 control over which key buttons on KB are pressed. Only the later mice, that have software with them, whereby you can remap the mouse buttons to act like KB keys, have that ability. But i doubt that you've mapped your mouse buttons to act as "CRTL" and "C".
Crtl + C is Copy command, where data is copied to clipboard. Malware can easily exploit the clipboard, to transfer data along (out of your PC).
Fix:
You can try AV software, e.g MalwareBytes and the like.
But if that doesn't help, format your drives and make a clean Win installation. As of why i said "drives", malware can live on every drive you have connected to your PC, and not just the OS drive. So, only wiping OS drive may not fix your issue.
Oh, if the malware is BIOS rootkit, clean Win install will not help. What helps, besides wiping all drives, is also wiping BIOS chip aka flashing BIOS to newer version (BIOS update). On worst case scenario, you're looking towards MoBo replacement.