How to recover unallocated space on a flash drive?

What does show up when you execute "diskutil list" in the Terminal? Maybe post the output here:

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What do you find displayed in Disk Utility? In particular, select the disk and click on the Partition tab to display the partition in the pie chart. Does the unallocated space show up in the chart?

The easy way: Partition/format again:

in Partition choose: 1 partition, GUID Partition Table

Choose: Mac OS Extended (journaled) when you want it only writeable in Mac OS, else choose FAT.

The disk now probably is not GUID PT, but partitioned Master Boot Record. MBR is old and can handle at max 4 partitions.

It is about Partitioning not formatting. Did you try it?

that piece has lost the format.

try in Terminal

fsck -y

on the external

(file check and repair).