So my question is, is there any possible way of sending all the transactions out as one output to a new wallet in order for it to be smaller in size and the transaction fee to be lower?
Like it or not, fees are going to get even higher in next few years, so think about using some alternative option if you are constantly receiving smaller amount of bitcoin on many addresses.
Best way I found so far is to use L-BTC liquid network addresses, they will get consolidated for free using Aqua wallet, and when you collect enough coins and fees are not extremely high than you can swap them to on-chain Bitcoin.
Compatible wallets so far are Aqua wallet, Blockstream Green wallet, Jade hardware wallet, ledger wallet, specter wallet.
Even if it goes up for a few more months or even years who knows, there's a point where we will get small tx fees.