Question about hps & updated income

Id like some opinions here. Im looking at leaving my current credit union & moving everything over to another one. This includes getting a new credit card. This is my issue. I already have a hard pull & denial from Nov. It was due to insufficient income. Ive updated my income to more accurate numbers. The cu im moving to dosen't have a secured card option. Just student checking & cards, but im not a college student, so I belive I'm not eligible. I also don't know how much of an impact it would be moving my banking to them. Ive only used them for the savings account. I posted about the cards avaliable here last year & the opinions were that they were meh. My income is now around 20-23k year with a 750 fico. See the link for the card options. So my questions are as follows. 1. Will the hp from Nov impact me if I do apply for a card? 2. Will my updated income info make a difference? 3. If I can't get a secured card, what should I consider?

Cards being looked at https://harvardfcu.org/credit-cards/