tldr blue item/mandate/lucidity/dark seal then idk sofw morello deathcap banshees zhonyas whatever, absolute focus/gathering storm and ghost poro

I always felt like nami scales better with ap than anything else - heal/shield power isn't great because she doesn't heal much, cdr is ok but the main thing she does is the initial burst with e/w, and I never really find myself oom. Meanwhile she has extra ap ratios on everything with passive - it's 90 + 20% ap as movement speed. So if you have 200-300 ap you get 40-60 more ms. And her E has a 60% ap ratio for the dmg if you hit all 3, and a 5% ap ratio on the slow. Finally ofc they nerfed nami by reducing her w dmg and increasing the ap ratio in a way that breaks even at 200 ap and is better if you have >200 ap (so it's a nerf because it hurts early game, but it does slightly further incentivize ap).

For items it helps that you go mandate, which gives +15 ap per completed item. Dark seal also gives a lot of ap but I generally like it after mandate, both because mandate is important to rush and because you'll pick up dark seal stacks faster once you have mandate and can follow someone fed around and give them mandate. One problem is you want boots of lucidity too so you kind of run out of item slots, but fortunately games end pretty quickly anyways (and you don't waste slots on p*nks). Also for conserving stacks, it's easy to die to literally anything on nami so you kind of play teamfights ridiculously far back and only interact with allied champs with e/w; you don't go up and fight enemies.

According to the wiki mejais is a legendary item, so it's a cheap 15 ap with mandate...?

So your core is support item/mandate/lucidity/dark seal. That's 4 slots...if you're going for instance staff of flowing water you have to sit on gold instead of all 3 components which isn't great but idk. I'd just juice (as pobelter would say) the deathcap except as a support you generally back without 1250g. Hextech alternator seems perfect with the e/w playstyle midgame, and it didn't used to build into anything good but now it builds into morello, which I'd prefer over chemtech now because it gives 90 ap vs 40. As is true in general, sofw is usually good, censer is usually bad. Fiendish codex is good and as a defensive item banshees or maybe zhonyas could be good since q/w are too slow to self peel vs anything.

For runes absolute focus and gathering storm because we're scaling guys and ghost poro I actually think is pretty underrated - it gives 30 ap (like 650g) relatively quickly as long as you're not losing vs an umbral glaive user like pyke or graves. I tried first strike and it seems bad (how could gold from dmg be balanced on viktor/karthus and still good on nami). Aery mostly shields since you start with e/w allies, but meh at least it procs sofw. Kinda curious what percent of comets would hit...