Three caveats before I dive in a little.
First, Nootropics effect everyone a bit differently (and Adaptogens as well, which I'll cover a bit as you mention quite a few), so as with my usual advice start with one or two to gauge how they benefit you (positively or negatively) and then move forward from there.
Second, autoimmunity isn't my specialty so take everything mentioned with a word of caution, research, and consult with your doctor as necessary when implementing anything (if you need to and it helps depending which way you go studies in hand can help explain your rationale).
Third, with anxiety, stress, overthinking, or things of that nature non-supplemental approaches can vary widely, but be extremely effective too. Depending on the type of stress and your response, things like meditation, quiet time, Heart Math, etc. That said this is a supplement forum so I don't want to get preachy and act like you can't benefit from supplemental action too.
Ok so I don't think I can cover everything in your list, but I'll try to go over things I've found beneficial for myself, others, and potential research for them. I think without getting into specifics that Adaptogenic compounds may be things you want to look into overall, as they "modulate" your response (up or down) rather then just amping everything up, depending on the stressor/scenario.
Mushrooms. I think honestly this might be a good category for you. Initially just thinking mental, anxiety, and immunity something like Lions Mane sticks out to me. Generally thought of for mental benefits, it also has some anxiety benefits and is an immunomodulator. If looking for a little stronger immune benefits, but probably lesser for anxiety and mood then Reishi comes to mind. Those would be the first two I'd check out, but feel free to look into all the mushrooms and mixes.
Adaptogen or herb wise I'd keep Bacopa, Ash, and Rhodiola in mind. Bacopa has stress, anxiety, memory, and attention benefits. Ash has so many benefits it is hard to narrow it down, but its overall stress benefits widely effect other areas too. Finally, Rhodiola seems to decrease fatigue (both in physical and mental areas) and that reduction has shown increased cognition, relieved stress, and small focusing abilities. With these herbs keep in mind standardization is important. 50% bacopasides of 150-300mg full plant seems a good dose, Sensoril or KSM-66 for Ash, and looking at salidroside and rosavin content (minimum 1% and 3% respectively with at least 250mg dose).
I could keep going, but that is a good start.
While I like to try things individually, once you have found things that work a well rounded formula for ease can be beneficial. I am a huge fan of SNS Stress and Anxiety (Bacopa, Rhodiola, Sensoril, and Theanine) if stress is the main issue (but will also have tons of other benefits based on those awesome ingredientes). Also have recently started Morphogen Adaptogen is a powerhouse. I plan to keep it in my arsenal for the mental, stress, and immune benefits.
