This seems at first glance at least potentially doable.

Create a website with content that’s only rendered with JavaScript and embed a miner.

Your challenge is to get the work product back, but you might be able to create dynamically generated URLs that show up in your logs as the work result.

You’d have to find a way to chunk the work and make it such that the work required is enough to be valuable to you, but not so costly as to stop the crawlers from using your site.

I suspect that in order for this to actually happen you’d have to have a significant infrastructure to deal with the crawler load, which you could instead be using to do the actual work.

Ultimately I suspect that this is the software equivalent of a perpetual motion machine, cute in theory, physically impossible.

Good luck!