If Disk Manager says "No media", it means that your flash drive is probably dead. What usually happens is that flash drive manufacturers use the same controller chips as the ones you would find on a card reader (e.g. SD card reader) in flash drives, even if the flash memory cannot be removed.
Then, when the flash memory dies, or some hardware issue occurs, the controller detects that it can no longer write to the flash memory and falls back to one of the default behaviour of a card reader, which is to declare that the "flash media" is no longer present, which is what Windows also reports as a result, as per your screenshot.
Unfortunately, since this is indicative of bad flash memory, you probably won't be able to reformat your drive. You may try your luck at locating manufacturer-specific low level restoration tools (but these tools are usually kept private and not made available to the general public) to see if you can reset the internal flash drive controller into "re-mounting" the flash, but you have to bear in mind that you most probably have bad flash memory on this drive, therefore, once you write to one of the bad flash blocks, you'll probably run into the same issue again or get data corruption.
You may also try your hand at reformatting your drive in a different OS if you have one (e.g. Linux), just in case, but by the looks of it, since it seems your flash memory is defective, you're probably better off using a new flash drive.
So, to summarize what probably happened:
- While Rufus was writing data, it happened to do so on flash memory cells that were defective
- The internal flash drive controller detected that the flash memory was defective because the operation failed to complete, tried to recover (there's usually a wear-levelling algorithm that can declare a handful of memory cells as defective and try to use spares... but that will only work as long as there are spares to be used), failed to do so, and, because the flash drive controller firmware is designed to work both for a flash drive with non-removable memory, as well as a card reader, with removable one, it fell back to card reader behaviour, and declared that the flash memory had been "removed".
- Windows, which doesn't handle card readers any differently than flash drives, got notified that the "media" had been removed, which of course prevents you from reformatting it or accessing any data on it.