ME TOO!!!
I've met this many times recently. It started with my quipped Legendary(or Iconic?) weapons, and then it also happened to my clothes.
I've been trying to figure out how to reproduce it exactly, so I checked out my weapons' dps every couple minutes and also made a quick save if it's normal. With this, it has happened twice now, and I'm pretty sure the true situation is this:
I have a normal savegame A that I came out of a store, checked the dps, and made the save a couple minutes ago.
After this couple minutes, before I enter a mission area, I made another savegame B, and then I died in the area and load the recently savegame and check the dps immediately.
That's when it happened again! THE DPS IS BROKEN! My weapon 1 Skippy's dps become 88 and all the legendary mods got randomized to common or rare ones!
Guess what, loading the savegame A won't fix this, I even tried to disable all my mods or verify completeness with steam, nothing helps.
I also tried what you said with the stash, I use a mod to remove the Skippy's quest mark, put it in the stash and get it back, the dps is back to normal now, but this doesn't affect the old savegames, I loaded the previous savegame A, it's still broken!
It appears that, somehow the issue just changed all my recently savegames and broke all them's the weapon 1??? The first non-broken savegame I can found is 30min ago, all the savegames after that is broken and the dps is all 88 with the mods rarity randomized.
I've met this enough times finding it really an annoying issue now, the weapon level can be reset to normal with V's stash, but still I had to use a Simple Menu mod to remove the quest tag and reset the mods to legendary.
Update:
I've just compared a normal savegame and a broken one, the difference between these two's weapon 1 is that, the borken one has no "Stat Entry"??? Maybe that explained why I cannot upgrade only the level of this weapon with Simple Menu but can upgrade both "level and rarity"? Is there any mod can mess with this "Stat Entry" and broke the savegames causing it not showing the problem until a reload?
When the issue happens, the dps is wrong, unequipping has a problem that it's still in the slot until a reopen of the inventory, it can't be upgraded with "level only" from Simple Menu, bla bla bla...... And "Create Stat Entry" indeed fix the weapon except the level is still 1, the unquipping works right again, it can be upgraded with "level only" again. Still tracking what excatly causing this.