Question regarding Capped Calls for Convertible Bonds

Hello all,

I just recently learned about capped calls as a way to effectively raise the strike price for convertible bonds. I understand the part of buying a call with the same strike/maturity as the convertible bond but am having trouble with understanding the rationale behind selling a call at a higher strike price. Is selling the call a way for the premium received to offset the premium paid for the call with the same strike/maturity at the note?

What if the stock price rises above the lower strike? In my understanding, the original bond investors convert their bonds, triggering the issuing company to exercise their lower call option and buy shares at the strike to issue shares to OG bond holders (cancelling dilutive effects)

What if the stock rises above the higher strike? Is the issuing company then on the hook to sell some shares to the bank/counterparts that bought the calls? Does the “protection” of a capped call stop there?

Also, is the premium effectively raised since the layer of protection from the bonds being converted is now at a range from the lower strike priced call to the higher strike?

Please let me know if my rationale for any of this is off. Thanks I’m advance!