No matter what save slot is used, expedition rewards are unlocked account wide, so old, present and future saves can claim the rewards.
Other items that behave this way are anything bought with Quick Silver, you won’t need to buy them again on a new save, just go to the Synthesis Companion and re-claim them. Then prepare yourself for a flurry of blueprint learned sounds. Some people use a trick of having multiple saves, to bypass the QS daily earn limit.
The recent patch seemed to fix a lot of saves that were broken around the time the Aquarius update arrived so rest assured they do find ways to make them recoverable and have fixes applied across the board via a patch.
An optional detailed breakdown of savefile structure…
(not required reading so don’t sweat it)
Think of your save as having a heirarchy in three-ish tiers.
The top tier is like a container that contains all your unique playthroughs, this will remember what QS rewards, Expeditions and Twitch Drop events you took part in or purchased.
Below this, the second tier, you have your list of unique playthroughs, these are the save states you select from the Main Menu.
Right now your list should have your broken save up the top as most recent played, followed by an empty list of “start new game” and/or a collection of previous playthroughs you may have started/abandoned/etc.
Within those saves, once loaded, there is then a third tier, which is the autosave/manual save state of that specific save you have loaded.
I’ve never seen someone with a broken save where the top tier is effected and you essentially have “no save” data. So as long as this didnt happen (can it happen? 
) you should have no worry of not getting the expedition rewards once your main save is fixed.
edit:
If they send you back a fixed save file, rather than fixing it via a patch, using this save file will overwrite any progress made, so this method you would lose any expedition rewards earned since.
If they do get back to you with a fixed save state, I would wait for the next patch to see if they applied it as a fix for all (and yours wasn’t just some very unique case) before over-writing your Curse Expedition rewards. Or if at all possible, you could share it with someone on here before transferring it over to your console and a save editor might be able to be used to unlock the expedition rewards for your fixed save for you (I feel confident enough to say I might be able to figure out how to do that should it come to that, or at least link you to a guide on using save editors on PC with console saves.)
