People just need to get used to paying for the web. Monthly subscriptions for Spotify or Netflix are widely accepted, so a fee to fund the rest of the net doesn't seem beyond the realm of possibility. It could even be made part of the ISP fee (perhaps this could be forced on all ISPs by govts under the guise of 'supporting local websites').
The technical solutions already seem to exist, but have been shut down 1) due to lack of use and 2) by the entrenched business model (in the case of Scroll). Therefore, the challenge currently lies in bringing the masses over to this business model (IMO easier than it may seem, as the masses never consciously opted for their current method of paying anyway and hence feel no attachment to it), and stopping anti-competitive take-overs by companies from the entrenched business model (currently enabled by regulatory capture, an even deeper root problem whose solution would solve many issues beside this one).
So assume that everybody switched to this model of funding overnight. I don't think it would stop surveillance capitalism entirely since the surveillance technologies that the current business model lead to being developed (AI, cookies, etc) have since been adapted for use in other settings (facial recognition CCTV etc.) whose investment sources are now entirely separate from the web’s. What's more, websites would probably keep spying on paying users anyway, simply because they already have the technology to do so, and it would make them extra money on top of their allocated subscription money. Despite this, I still think it's a change worth working towards.

I cancelled my Kagi subscription as soon as they started rolling out their "AI" features.
Edit: Otherwise I was happy to pay a monthly fee for privacy respecting search. Now I use a mix of 4Get, SearXNG, Startpage
Oh :(. Looks like they must have still viewed you as a product rather than a paying customer... It seems they must have calculated that training models on your data and selling those would make them more money than just raising the price of the subscription. I suppose the structural problem then is that selling your data is something a business can always do to make a buck regardless of if you are (or aren't) already paying them.