How to fix an unresponsive iPhone 11 screen?

Try the force restart again. The key is to keep holding the side button in the last step until the Apple Logo appears no matter what shows on your screen. This could take up to 20 seconds. It sounds like the side button was briefly let go and when pressed again, Siri was activated.

Force restart iPhone - Apple Support

The Force Restart always works unless there is a hardware issue with one of your keys which is not very common.

Antonia_Scott wrote:

how long should you hold the volume up and down buttons for before releasing?

I assume you do this simultaneously?

Nope. Press and quickly release the volume up button, then press and quickly release the volume down button. Then press and hold the side button for up to 20 seconds until the Apple logo appears, ignoring anything else that appears on the screen. It usually takes a couple of attempts to get the speed and sequence of the key presses correct.

Antonia_Scott wrote:

how long should you hold the volume up and down buttons for before releasing?

I assume you do this simultaneously?

No.

Follow these steps:

In rapid sequence, press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the side (power) button. Only when the Apple logo appears (it might take 10-20 seconds), release that button (ignore all other screens that might appear, the one with the "slider" to turn the device off included).

Regards

Giulio

You can also try to connect in Recovery to your Mac, to restore your device, in case this is software related:

If you can't update or restore your iPhone or iPod touch - Apple Support

All's well that ends well :)