I recently installed a mod called Trinkets.
The backpack I was wearing disappeared because of the new equipment slot.

I found the .dat file of the backpack before it disappeared in /backpacks in the world folder. Can I restore the backpack?

Yes you can try restoring from this file, but Id suggest different solution. Latest travelers backpack updates provide option to retrieve backpack when back slot mod is installed during gameplay. So you can update the mod and backpack icon will appear in your inventory to be retrieved. Or you can simply go to esc -> mods -> travelersbackpack -> config -> backpackSettings -> trinketsIntegration/backSlotIntegration (naming depends on mod version) and set this option to false. You will be able to access backpack again. If you play on server, then this config change has to be applied in server config to make effect.

Oh! Thank you! It saved me.
But some players said they couldn't recover.
I need to know how to recover from .dat.

Make sure they update the mod on their pc too
https://github.com/Tiviacz1337/Travelers-Backpack/wiki/Commands#restore-command