The challenge of reducing the dependency of fossil gas differs between the Nordic countries. Therefore each country has its own set of challenges to solve.
Norway exports while Sweden and Finland imports gas
Denmark is connected to central Europe and receives the gas mix in the grid from both Russia and Norway. (The Danish gas production is temporarily low due to maintenance of the Tyra Field).
Finland gets gas directly from Russia and through Estonia.
Norway exports a large amount of gas mainly to central Europe and partly to the Danish grid.
Sweden gets gas from the European grid through Denmark.

Fossil gas use differs between the nordic countries
In Denmark around 350,000 buildings are heated by gas, and switching to district heating or heat pumps is a major task in the years to come.
Finland primarily uses gas for electricity and heat production and industry, especially pulp and paper and iron and steal production consumes large amounts of gas. Switching to green energy sources in these processes is the primary task for Finland.
Norway does not have a high domestic gas use in the society as such, but the fossil fuel extraction uses a large amount of gas today. Electrification of the energy production can reduce the fossil gas consumption substantially.
Sweden mainly use gas for non-energy purposes such as fertilizer and plastics, but also for process heat in the iron and steal production, chemical industry and pulp and paper production.

If you want to dive into more details on the role of fossil gas in the Nordic countries, you can find the full analysis here. The analysis is made in collaboration with IVL and Energiforsk.