What further steps will look like if this spam continues?
Bitcoin's price will continue too. 
I don't remember this happening before in history
Remember the time when ICOs have been that much and it has affected the ETH network. The fees for a coffee was about $10 and I think we're going back to that time.Because IIRC, the fee for Bitcoin transactions during that time was also high back in 2017 bull run.
2017 was from natural demand causing a busy network, or miner manipulation to capitalize on fees. It could be the latter now but I am quite sure the the current situation is a sponsored attack, more than it is just a busy network.
Since 2017, most networks have implemented improvements to make them increasingly scalable. It is unlikely that purely legitimate blockchain network traffic will cause a prolonged spike in fees, especially with available layer0/1/2(and now 3's) that are available.
What further steps will look like if this spam continues?
Bitcoin's price will continue too. If we're talking specifically about a network stress attack, then actually, it can stall price movement and additionally effect sentiment, as it temporarily highlights a flaw in usability and scalability for Bitcoin. It may be good for altchains that are more scalable, like ETH. It depends on the trajectory of the attack.