So I'm convinced the mutation we see is actually just the symbiote. 

Let's go over the facts:

\+ Peter gets physically stronger 

\+ His eyes turn black

\+ He is resistant to telepathic attacks

\+ He has organic webbing 

\+ He gets more aggressive 

The symbiote can give him all that. The symbiote also has a personality and so if it notices its host in distress, it may react. We see the transformation start to happen when Peter experiences an intense psychological stressor. Perhaps the symbiote got pissed and started to react. 

It has been about four years since the drop of the symbiote found its way to the main MCU universe. It has had enough time to seek Peter out. It also expressed a desire to find him in the post credit scene of Venom: Let There Be Carnage (or maybe it was Far From Home? I forget). 

But why hasn't it shown up in a meaningful way yet? It was one drop so maybe it was reduced in function and needed time to grow again. I can't say for certain, but it could've remained dormant because of something like that. Maybe if it left more behind, it would be more active.

Here's what I see coming: Secret Wars rolls around and we see Spider-Man placed into a very dire situation. His eyes turn black and he puts on a better fight, but ultimately loses. He digs deep like Cap did against Thanos in Endgame. The black in his eyes begins to expand from his eyes and across the rest of his body. The symbiote reaches maturity under stress and we are finally given the Tom Holland black suit Spider-Man. 

Theory about Spider-Man Brand New Day. Spoilers within. Beware.