The Pages files are likely still on the flash drive and can be retrieved with a reliable flash drive data recovery tool that's compatible with your Mac's processor & operating system and your flash drive's file system.
I highly recommend you try iBoysoft Data Recovery for Mac. It's a professional data recovery app that enables you to recover Pages files and other types of data from flash drives, hard drives, SD cards, etc. It's also compatible with Intel, T2, M1, M1 Max, M1 Pro, and M2 Macs running on Mac OS X 10.11 El Capitan and later operating systems.
This flash drive data recovery software supports restoring files from external drives formatted with APFS, HFS, HFSX, HFS+, FAT32, and exFAT. It's easy to use, safe to install, and has an excellent recovery rate.
Besides, it allows you to preview found files on the flash drive for free. Follow the steps below to recover the Pages files on your flash drive on Mac:
Step 1: Grab the free download of iBoysoft Data Recovery for Mac from the button below and install it.
Step 2: When the app is launched, select your flash drive and click "Search for Lost Data."
Step 3: After the scan is complete, you can preview the files it found.
Step 4: Check the box next to the Pages files you want to restore, click the Recover button, then save them to a different location.
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