How do I factory reset an iPhone 14 that no longer works?

See "Remotely erase your iPhone or iPad" here.

Find your lost iPhone or iPad - Apple Support

The better approach would be to deliver your iPhone to Apple where if you choose not to repair it, they will recycle it free of charge.

how can I ensure all my information is erased if it's fixed?

The repair process will erase all of the data on the phone, so if you decide to have the screen replaced, the iPhone will be returned to you as a refurbished phone that will be ready to be set up again.

It would be redundant, but you could erase all of the data on the phone again if you wish.