Is it possible to use a broken phone screen with my laptop?

It really depends on your phone's brand. If you're using an Android device, you might try a tool like Screencopy to mirror your screen to your laptop. However, if it's an iPhone, your options are unfortunately pretty limited. It's best to consider getting it repaired at a local shop, as that could save you a lot of hassle.

You could also think about getting a phone docking station with HDMI output and connecting a mouse and keyboard. After that, load a VNC application on your laptop to control the phone. Just make sure your phone model supports this option.

If your phone supports DeX mode, that could work well too. I found a dock that connects my Samsung phone to a monitor, allowing me to use my mouse. Just a heads up, certain apps like Google Authenticator may be blocked if the screen isn't functional.