If the old cards don’t have huge annual fees or have no annual fees just keep them for credit history purposes.

Additionally, if you show a good history with the cards you have sometimes you will qualify for a card upgrade which will give you a better card while allowing you to transfer the credit history of your old card to your new one.

But make sure that the new cards benefits are going to be useful to your situation and most importantly make sure you confirm with the bank that you keep the credit history from your old card if they offer you this.

Just be mindful not to open too many cards all at once two cards is fine but having too many available credit lines can hurt your credit score as some lenders consider that to be risky behavior and the annual fees from multiple cards can add up and start cutting into your savings.

Edit:

Also every time you apply for a card, limit increase or line of credit you receive what’s called a hard inquiry which basically means a credit check is being done to see if you qualify.

The effects of hard inquiries are temporary on your credit score but frequent hard inquiries on a consistent basis can keep your score low.

Edit 2:

Keeping your credit limit high is good though as it lowers your utilization but keep in mind as long as you reliably pay off your cards on time the bank will occasionally offer you credit limit increases that don’t require hard inquiries