No. Unlike Street Fighter 6 or Guilty Gear Strive, Samurai Shodown (2019) does not support cross-play. Switch players can only fight other Switch users. The update only improves network reliability within the same console family.
After downloading, your game info page should list: samurai shodown switch nsp dlc update eshop full
This is the legitimate equivalent of the "full NSP" — a complete, playable digital installation. This is the legitimate equivalent of the "full
While not the main fighter, the eShop also sells a perfect port of Samurai Shodown! 2 for the NeoGeo Pocket. If you want the “Full SNK aesthetic,” grab this NSP as a companion piece. DLC Pack (separate purchase/download):