First of all, trade at the Norwegian-Swedish border is mostly a one-way phenomenon. Since prices in Norway are usually higher than in Sweden, people from Norway often go to Sweden for shopping, but not so much, or even rarely the other way around. There are even many shopping malls along the border on the Swedish side, targetting specifically Norwegian customers.
That led to it being common, at least a while ago, that most shops at the Swedish side of the border accepted Norwegian cash, but it was much less common that shops at the Norwegian side of the border accepted Swedish money. Even if the currencies right now are almost valued the same, the Swedish crown has at least for the last 20 years usually been worth more than the Norwegian crown and Swedish shops have always taken the difference in exchange rate into account, usually with an unfavourable exchange rate.
As JonathanReez already commented, cash is rarely used in Sweden anymore and it's the same in Norway. It is still very unusual that shops do not accept cash at all as payment, but I would not anymore expect it to be common, that shops in Sweden accept Norwegian cash.