In the future the cost of transactions with bitcoin will be similar to now, the reason is simple, it may be that in the future the price of bitcoin is high then their fees will be high and if the price is low, the fees will not be so high, not only in mining, because there may be many miners with very large solar cells but in the same way the Exchanges will charge their corresponding fees according to the bitcoin price for the moment.
In the future its expected that the value of bitcoin and other cryptos will be super high because they will be indemand therfor the price of transaction fees will also be super high and it does not matter if the miner uses a solar power or not because miners will still choose the best highest possible fee so that they can profit easily and their effor of mining a transaction wont be wasted . however at some point i think your also right because in the future the value of cryptos are still volatile same as today .
That would be the relation between price and possible fees. It is a common thing to happen as miners will urge people to pay it high otherwise they'll never process their transactions or causing long delays due to prioritization. That is why I've never wanted it to be more expensive cause it came into the point that we can't afford it to buy and transaction fees will stay at low.