There seems to be some kind of item chaining system. When a lot of items are auto-collected in a short time, effects happen, such as some kind of multiplier (UFO-style value increase?), and the appearance of a bomb part. Or sometimes a life part. Not sure what determines the exact reward. It may relate to the quantity of items collected.
The starting number of bombs has returned to 3. You also get a free bomb part after every boss phase, like with SA's life parts, complete with it not appearing if you die on that phase, I think. Plus an additional bomb/life part after spellcards because of the point items the boss drops.
Bombs auto-collect items again like in LLS-MoF (seems to preserve maximum value like UFO/TD auto-collect, but it's hard to tell). It seems they also can trigger chains, allowing for the possibility of bombing for life parts. The bomb seems quite short, more like a border break, with no Sakuya-specific details, so it may be the same for all characters like in MoF (edit: actually, as several others are saying, it seems to function like SA MarisaC's bomb with an extra screen clear, giving you 3/8 of a bomb back if you don't break the border, not sure how I missed that). It's also used as the death wave. (Dying is the same as in UFO otherwise, -1.00 power, with .07 scattered.)
Canceled bullet value is quite high compared to SA/UFO/TD, though still lower than MoF. It seems to be the primary method of increasing PIV (though that might just be because the player isn't actively scoring).
On the topic of PIV, it seems to only start at 10,000, instead of 20,000 on Lunatic like in UFO/TD.
Spell bonuses are 9m/12m/15m in the video, and 13m for Hard stage 3 in the earlier screenshot. Tentative formula = (3 * stage number + 2 * difficulty value) * 1 million. Definitely more emphasis on spell bonuses here. Also stage clear bonuses have been increased: stage number * 3 million. Still not that high.
Oh, and that shot type is SakuyaA. It's visible when the player saved a replay at the end.
