How do I find UK employers that actually sponsor Skilled Worker visas? Is there a list?

Yes. The UK government publishes the register of licensed sponsors on GOV.UK, listing every employer allowed to sponsor Skilled Worker visas. It shows who can sponsor, not who is hiring, so use it to check companies before applying. Cross-reference it with job boards that filter for "visa sponsorship." One warning: if anyone offers to sell you a sponsored job or Certificate of Sponsorship, it is a scam; genuine sponsorship is never bought.