@hundido :-
One question - if I may? What size is your flash drive? Because I've NEVER seen a flash drive that small before.....
What would help enormously is a screenshot of gParted, showing what you say is your flash drive (sdb2..?). And if what I see in the corner of your first image is right, it looks like you've got at least 3 USB devices plugged in.....and every single drive in your system is either exFAT or FAT32 (aka vfat). What ARE those other USB devices, please?
These are not Linux file-systems, they're Windows file-systems.
Now, Puppy CAN run from a FAT32 partition, but it then needs to use a 'save-file'. This 'save-file' will contain a complete Linux file-system inside it. A 'save-FOLDER' requires a Linux-formatted file-system to already be in place before it can function.
If Puppy detects a FAT32 file-system, by default it SHOULD only offer the 'save-file' anyway...... We need to know for definite which of those USB devices is your flash drive; to me, at least, I cannot concur with your assessment without knowing what those 3 USB devices are supposed to be.....
---------------------------------------
Ummm.....curious. Where's sdb1? If you have an sdb2, there must, logically, be an sdb1 ahead of it.....so where is it?
From the screenshot, it would appear that your main system drive is a 1 TB NVME SSD, which is formatted as exFAT. Puppy is showing it twice, because sda1 is your primary system drive, but Linux always lists flash "block" devices separately.
'nvme0n1pn' would, on the face of it, appear to be the required UEFI 'boot' partition on the main drive.....but if it IS, I don't understand why the main system partition is then sda1. It should be sda2.....
We definitely need a screenshot of gParted, showing your main drive.
(Others will have to take over from here. It's WAY past my bed-time!)
Mike. 