The 'best' trick I learned from someone over here when working with Claude Code is to very regularly go back a few steps in your context (esc esc -> pick something a few steps up) and say something like "yeah, I already did this myself, now continue and do Y"

It results helps keep the context clean while still keeping the initial context I provided (usually with documentation and initial plan setup) at the core of the context.

Now that you say this, I did notice webpages blow context but didn't think too much of it just yet, maybe there's some improvement to be found here using a subagent? I'm not a big fan of subagents (didn't really get proper results out of them in my initial experiments anyway) but maybe adding a 'web researcher' sub agent that summarizes to a concise markdown file could help here.