It's hard to convince people who have grown up or bought into the myths about credit cards, e.g., that they're evil, you'll ruin your credit, go into debt, etc. As long as you treat credit like cash, spend only what you would on credit cards as you would buy in cash, pay off the statement in full at the end of every month (some even go in to pay off every week), you can use credit to your advantage. Cash doesn't earn you anything on the money you're spending anyway so you're leaving a lot of value on the table, whereas credit cards come with signup bonuses and rewards for that spend.
When you apply for a credit card, almost all issuers will conduct a hard pull or inquiry of your credit report(s). Personally, a hard pull causes my credit score to drop 2-5 points temporarily. That's negligible! My credit scores fluctuate that much month-to-month just from changes in my balances from regular spending. And if your score is excellent (over 800+) or even very good (~750+), a 2-5 point drop will not affect the rates you get for loans or anything else. (I've never heard credit scores affecting car insurance rates.) A hard pull remains on a credit report for 2 years, but the effect of a hard pull dissipates in a few months.
Credit scores go up and down for a number of reasons, from changes in your credit card balances, to credit utilization ratio (how much balance you have vs. amount of available credit on your card accounts), to the average age of your accounts (the higher AAoA, the better). If you're opening a new personal credit card, you'll take a small hit from the hard pull and your AAoA will drop a little, but you're opening a new account that will increase your available credit lines, and assuming you don't spend any more than you usually do, that would have the effect of lowering your credit utilization ratio, which tends to increase your credit scores. A business card like the CIP will not appear on personal credit reports, so you won't get the benefit of having that biz card's credit line increasing your available credit, but it also won't lower your AAoA, and any balance you put on that biz card also won't count against your credit utilization ratio. For example, when I was paying most of our expenses through Plastiq (when it was still coding 3x) on the CIP, I was barely using my personal cards and the credit utilization ratio on those personal cards was like 1-2%. My score slowly went up from ~800-810 to ~830-840. My scores still hover around the high-810s to mid-820s now.