Manila to Beijing to Tokyo

You are definitely eligible for 144 hours visa free transit assuming that you are US citizen. Your route: Hong Kong - Beijing - Tokyo is exactly what the transit means. Please, just have in mind that you are not looking for a "transit visa", but for "visa free transit". It is important to use exact terminology to avoid any misunderstandings.

Yes, you can because you are perfectly eligible. By the way, you will travel covered by 144 hours visa free transit and you will not receive any kind of visa. Please, have this detail in mind to avoid any possible misunderstandings.

Your flight itinerary is definitely eligible for 144 hours visa free transit. Please, just use exact terminology, i.e. "visa free transit" and not "transit visa" to avoid any misunderstandings because you will really fly, make a transit and stay in China visa free.