Can I retrieve files from old phone that screen is damaged?
My old rooted phone has a smashed screen but can still turn on. It's not worth the cost to repair it.
I can get to the lock screen but can't enter the lock due to the damaged screen. As such, it doesn't actually appear as a mounted drive when connected to a PC.
Can I retrieve files from inside it or even run a backup to get the latest text messages?
If you can still use adb (since you put 'adb' tag in this question), you may try vysor ( https://www.vysor.io/download/ ) so that you can redirect your Android screen to a window on your PC. That means you can use mouse-click instead of finger-touch to operate your phone.
After that, try to backup your old phone to the network (since now you have the PC as your new screen to operate your phone), and retrieve your backup from your new phone.
There should be some similar android to PC screen (alternative to vysor) software.
Disclaimer: I do not stand for vysor software. Please use it at your own risk: i.e. I am not liable to any damage, identity theft, hacked phone, any charges on the use of the software, to name a few.