To be more energy efficient, wouldn't be a consensual fork - right now - without the reward of new mined btc for each block helpful? As the reward is lower, less effort is spend in mining new bitcoins. How the transactions fees will evolve would be quite crucial the get the miners activity down (and their energy consumption). I would assume that the transactions fees would stay at very low levels, because every miner has always an incentive to add any transaction with a positive fee.
Additional question: For sure there are some cryptocurrencies which reached that state (of no mining new coins). How did the transaction fees evolve after mining the last coin?
I would assume that the transactions fees would stay or converge to be very low levels, because every miner has always an incentive to add any transaction with a positive fee.

Block space is finite, so users are bidding for their position within the next block. Miners will always choose the transactions which have the highest feerate because it makes their income the highest. Today the fee rate often makes up a significant ($100k+ USD) portion of the total block reward.

https://mempool.space/

How the transactions fees will evolve would be quite crucial the get the miners activity down (and their energy consumption).

Mining activity would reduce naturally if there was less reward, but there's no opportunity for changing core principles of Bitcoin like this.
As a valuable currency Bitcoin needs to be predictable and justifiable, if the rules dramatically changed it would make a fairly lousy currency. You wouldn't be able to invest in mining hardware for example, if you couldn't model even the base income a couple of months into the future. Making even small changes to the economics of the system opens the floodgates for others. ultimately.

For sure there are some cryptocurrencies which reached that state (of no mining new coins). How did the transaction fees evolve after mining the last coin?

There's no useful comparisons to be made, nothing has the scale, maturity, and properties of Bitcoin.