I'm not saying you should lie when applying for credit cards, but I'd like to think if I were in possession of a NOA showing $150K income for the prior tax year and was particularly recently retired with let's say some sole trader income at a young age, I might identify as self employed for the purpose of said application form
Imho retired without a pension or superannuation annuity is really only a state of mind. I don't think what you think of when you tick retired and what they think of when they run it through their model are that well aligned. Similarly, I don't necessarily think rental income is rental income unless I'm filling out my income tax return form... Of course associated loans need to be disclosed along with expenses but if you are talking about 50K pa of passive income after expenses, that's not any different to a small business owner making 50Kpa of profit. It isn't enough to qualify for some of the more premium card offers but if the minimum income threshold is met, that is your income.... A NOA will say that is your income, too. I am sure your situation could be viewed through another prism.