Dividends and capital gains taxes are only part of the equation. You still need to solve for corporate income tax somehow.The whole value of non dom status is to benefit of tax free dividends and capital gains. If it is impossible to receive the dividends of the offshore company tax free and without further questions the non dom status is a joke. In relation to previous obtained personal assets the tax office will receive the info via AEOI, will they began to ask any additional questions regarding these assets?
Your company might qualify as tax resident in Cyprus (especially if it's some useless IBC-style entity), and as such you'd be legally required to pay the 12.50% corporate income tax rate or work something out under a DTA. Enforcement is very, very relaxed on this. They don't spend a lot of time chasing non-domiciled residents running offshore companies. But in return, you shouldn't be a burden on society, which is why it's recommended you have a private health insurance. Quid pro quo.
However, most people I encounter tend to start companies in Cyprus instead because it's easier when it comes time to pay tax and grow a large business. You can remove yourself from public record through nominees/trustees.
If your personal assets are in your name (in a personal bank account), I can't think of any situation where Cyprus would ask you any questions. But if you do bring in funds which are untaxed or otherwise illegally obtained, this can be a problem if for some reason you are audited. Which, AFAIK, is practically unheard of.
Keep a low profile, follow the law, and be a good little expat and they will leave you alone.