The impact of having heavy economical sanctions in a country can quite be costly- it will be relatively harder and difficult for the people in Russia to transact and purchase goods within their area. Inflation will rise and all of the costs of goods would definitely spike-up due to having scarce resources on their countries.
This is where BTC can step in. Its application can somehow support Russian citizens to purchase goods outside their country by transacting and using BTCs. I do think that BTC can have an impact to this war especially on its price.
They can use bitcoin to order stuffs online but I'm thinking if how can a delivery pass through on their country? because this Russia is now blocked for incoming and outgoing transactions. There's also talks that bitcoin transactions which came from Russia is going to be restricted, this includes some exchanges and maybe some wallet providers. They really want to make sure that Russian country would suffer and won't escape the sanctions that have been applied to them.
Bitcoin can be used in tough situations but only as an alternative to national currencies and once the situation returns to normal, I'm afraid that the use of bitcoin can become weaker.