Surprisingly the fees still low, it's high likely big companies buy Bitcoin in bulk and people who have Bitcoin didn't want to sell it. It's make sense though, we know the peak of Bitcoin after supercycle are on months 10-12, now it's not yet the peak.
I think we would see the fees spike during that three months.
We might see spike or not. It all depends on who and who is moving their coins from one place to another. As it seems right now, most big bag holder has moved their Bitcoin to a cold wallet where it will be for a long time, so we are left with tiny amount of supply that are been move around by the retailers. Some exchanges are holding the rest while some are been held by some protocol as yield farming. As long as Bitcoin doesn't have any insensitivity, the mempool will remain scanty.
If in the next three months, the Bitcoin price continues to break more all time high, I don't think people will move their Bitcoin, the price you are seeing Bitcoin now is been targeted from here to 120k and the 130k to 150k, this is the only thing people are seeing and not reversal but if for instance Bitcoin price dump from $150k to $120k in a day without reversal, there is going to be more Bitcoin on the move and that will spike the mempool because short terms sellers will want to exit the market quickly.