The files that were overwritten in the first 3 seconds are gone. Though, It's likely that most, if not all the data is okay. Hopefully its just the pointers to the files that was over written, meaning you'll have to use some file recovery software on the disk/image to get it back. I don't have any software suggestions to do that.

DD nuked the partition info and the first several hundred megabytes of data.

Next time, I would suggest setting up Ventoy so you don't have to dd iso files to the flash drive anymore.

Phtorec can scan the drive and try to recover your remaining data. I've used it in the past to get files back from dying drives. Linky https://www.cgsecurity.org/wiki/PhotoRec

I used something called GetDataBack at an old MSP. If the file system is supported, it might work. It takes an extremely long time to run… just fyi. I usually duplicated the troublesome drive beforehand to an identical or larger sized one just in case.

A time machine barring that the data DD overwrote is gone. there are some theories around being able to recover things with an electron microscope but eh. You could repair the partition table and see what you can get back but its best to consider the data knackered. Sorry probably not what you want to hear but it is what it is.