How fast does Prime Energy regenerate?

That trickle is the only free source of energy, and it runs into a ceiling. The pool caps at 300, so once you are full the clock stops paying you. Anything the timer would have added while you sat at the cap is simply gone. The daily figure is lower than the cap, which means a full pool is not something you rebuild from empty in a single day of waiting.

What you spend it on matters more than the rate. Claiming rewards and drop materials from boss chests costs Prime Energy, so a boss you have already beaten still sits behind the meter until you pay for the chest. Plan your logins around that rather than around the fight itself.

The monthly pass raises the cap to 600. The regeneration rate does not change, but the larger buffer means you can go longer between sessions without overflowing. Real money also buys extra stamina directly and lifts the daily and weekly energy limits, which is the only way to move faster than the timer. The pass and its other perks are covered in full in the linked article.

Playing around the cap

The practical habit is to log in before you hit 300 and spend down, rather than letting the meter sit parked. Short, frequent sessions waste nothing. Long gaps waste whatever accrues after the pool tops out, and with the base cap that happens sooner than most players expect.

Not settled: Separate daily and weekly energy limits exist on top of the regeneration timer, and how those caps interact with the steady trickle is not spelled out in the beta build.