Hi!
Whenever you are in the 'Extras' menu (the tomb next to the character Omicron Arkh, on the command bridge) all DLC cosmetics should have so to say 'instructions' on them about how to unlock them, even if they are 'purchased'.

As for the missions, you can see what DLC campaigns there are in the menu accessed by talking to the character labeled the 'Astropath'. There, you can see that you need to complete a couple of things in-game (like unlocking a subsector on the starmap) before you can access their campaigns. Again, even if they are purchased.

Is it possible you need to do these things first? Sorry if I stated the obvious and we are way past this. If so, you've completed all pre-requisites, and you still cannot access your DLCs, would you be so kind as to attach a couple of screenshots of what you see in these menus that I mentioned?

Thank you for your patience and cooperation, hope you have a great day!

Cheers!