As @ap2 has said training is quite task-specific, so the priority for hiking hills with a heavy pack is to get out as much as possible and hike hills with a heavy pack. You want to incrementally increase your speed and the ground you cover - but listen to your body and don't push yourself to the point of injury. Failing that, climb stairs, but this is pretty boring so hit the hills if at all possible.
One way to enjoy the maximum training effect from your hiking is wind-sprints. A couple of times during the day, blast up an ascent as hard as you can for 20-30 secs till you reach your maximum safe heart rate. Then walk on slowly till you catch your breath. Repeat 2-6 times, working up gradually, as this is demanding. Only do this a couple of times a week or you'll overtrain.
A second tactic is bouts of pushing hard with your walking poles to tire your upper body and get some cross-training effect as you would on an elliptical ergo or Nordic ski-trainer.
In terms of general conditioning, a good deal depends on whether you are going northbound (NOBO) or southbound (SOBO). Going NOBO, the start is gentle and most hikers work up their mileage gradually as they find their hiking legs. Going SOBO you're in big hills from the start, and speed is vital if you're going to reach the Sierras before the autumn storms. So it's more important to be in hard condition and ideally, to have spent a couple of days acclimatising to altitude before you hit the terminus.
The other physical priority is injury prevention. The issues that are most likely to knock you off the trail are feet, ankles, knees and hips. I'm not going to go into detail here, but there are a lot of good bodyweight progressions on YouTube that will help you injury-proof your power train. Focus on good form. One thing you might miss though - recent research suggests that the best way to protect your ankles is to work on your balance. Search for "sport balance training". You could also take up slacklining. For training your feet (much neglected) search for "Toe-ga exercises".
To harden yourself mentally, be sure to go out in bad weather as well as good. Get used to spending multiple days on the trail in cold, rain and snow. If this puts you off, you'll know that thru-hiking is probably not for you...
More generally, experienced hikers, Rangers and SAR experts are increasingly concerned about the number of PCT hikers who are woefully underprepared in terms of skills. The trail passes through big, remote mountains. Weather can be savage, and you mustn't underestimate what you're taking on. Hope for the best but prepare for the worst.
You say you have backcountry experience so this may not apply to you. Though if you've mostly been in the woods, you should be aware that life above the treeline involves some additional skills. As this is literally a question of life and death, I'll add a checklist for any hiking newbie who is contemplating any of the big trails.
It's vital that you become competent in:
- Navigating in bad conditions with map and compass, as well as GPS.
- Judging snow conditions and moving safely over steep, icy snow.
- Crossing fast-flowing streams (this is a major cause of fatalities).
- Staying warm while walking in wet-cold conditions.
- Camping safely in cold, wet, wind and snow including cooking safely without burning yourself, your shelter or the surrounding forest.
- Personal hygiene on the trail to avoid gastric infections.
- Dealing with bears.
- And of course, a deep understanding of low-impact, leave-no-trace principles, as there are too many PCT hikers who are damaging the trail.
You owe it to yourself, your family and to the SAR personnel to be as safe as possible on the trail. If you are a newbie contemplating one of the Triple Crown trails and don't have the commitment to master these skills before you go, perhaps you should be questioning your motivation.
Hope you find this helpful - and perhaps we'll meet on the trail!