>>2824258 (OP)Get a sleeping bag that's way warmer than you think you need. I'd get a carinthia setup (if in EU) or a MSS (if in the US) if it needs to be cheap. I've used a Def 4 in -20°C (which is just slightly warmer than svalbad in winter according to wiki) with just a tarp before, and was comfy, but I know other guys who already doubled up with the Tropen by that point or went straight to the def6.
Outfits depend on how cold tolerant you are and how long you want to stay there. March is cold enough that moisture shouldn't be a problem, so personally, I'd take heavy wool or light furs, but that's mostly due to me being a larper kek.
For heat, you'll need a gasoline stove. Ethanol will freeze, kerosene will jellify You could get away with ethanol / gasoline mix in principle, but those aren't the safest. Better spend the extra 20€ on a proper gasoline stove.
tents I can't speak to, as I use a tarp or no shelter.
Iirc, svalbad has legislations about needing to be armed at all times due to polar bears.
Disclaimer: I've never been to Svalbad, or any arctic island. My experience is from european continental winters. According to wiki's climate diagram, those SHOULD be comparable to svalbad's spring, but no clue how true that is.