I currently have my BTC stored on a MultiSig cold wallet, which can't be connected to a lightning node. Do you think it's a better idea to move them to a lightning wallet like on electrum for example before the transaction fees get too high? I want to avoid paying a big amount just for one transaction in the main network
As there's no limit on the bitcoin price, similarly there's no limit to the bitcoin fees as well. Also there's no way to predict. You can check the mempool to see the current bitcoin fees.
Lightening network is a solution to it for sure. But it's a sidechain. If the bitcoin fees becomes higher than ever, it will somewhat affect the LN as well. Because LN also broadcasts the transactions in bulk. The Ordinals need to stopped once and for all.