First, we need to establish the primary motivation for cheating. People cheat to improve their odds in this brutal job market. A high Codeforces rating and strong competitive programming contest results has historically been a strong resume signal. For example, I know a higher rated individual who told me they, now regrettably, sold their Codeforces account to someone for thousands of euros a couple years ago when they were in financial need. Why would anyone pay thousands of euros unless there is a strong chance your investment will be returned?
Given this, I don't think some of the solutions I've seen people propose will work. Getting rid of ratings wouldn't be enough, we'd need to get rid of ranking lists for each contest. If ranking lists persist, there is still an incentive to cheat since cheaters can put strong contest finishes like top 1% or top 5% on their resume. Obviously, that's not desirable.
A better solution is to attach some form of identification to people's accounts. For example, on my account you can see my name, the university I attended, and my university email. If someone like me decides to cheat, at least they'd have to stake their reputation. Preferably, identifying information such as people's names should be verified by government or university IDs. Implementing such verification systems isn't particularly difficult with modern tooling.
Furthermore, reporting the identifying information of cheaters to employers would really hit cheaters where it hurts. An automated system can mass report cheater information to major employers across sectors such as quantitative finance, technology, banking, and more!
If you can't tell, I have the utmost disdain for cheaters. They are desperate dogs, no better. If we take steps such as the ones I've outlined, the cheaters that remain will primarily consist of devious children. Someone else can propose solutions for those kinds of cheaters.
If Codeforces would like help implementing such measures, I, and I'm sure many others, would be willing to help.
UPDATE: Just thought of a nice way to formalize my proposals. We need a two-tiered system, one with ID verified accounts and everyone else. The two types of accounts will be allowed to participate in the same contests, but unverified accounts should not have a field that says "Rating" in their profile, but rather, something like "Unverified Rating". To verify your account, you should provide some combination of your name, government ID verification, university ID verification, a selfie of your face, and your university/work email. There are services out there we can employ for proper ID verification, and all of the data is destroyed after the verification process terminates. Thus, anyone seeking to show off their Codeforces rating on their resume to get a job would be incentivized to go through the verification process, as employers will naturally be more skeptical of an "unverified" rating. Kids should not get verified, as why would a kid care about whether their rating is "verified" or not? This solves the problem of handling minor data, we won't have to.