Thanks for the additional detailed comments! Appreciate it.
Some deep Googling shows the fuel pressure drop overnight issue like you described, I think this part is prone to developing a crack that relieves the pressure in the FPR part:
https://www.fcpeuro.com/products/bmw...ly-16117195469
There's also the main fuel pump:
https://www.fcpeuro.com/products/bmw...ly-16117195463
To be honest I'm not sure which side the fuel pressure regulator lives on. RealOEM doesn't describe it. Also, I've not seen a fuel filter anywhere on RealOEM or FCP Euro or the other shops.
Does the N52 E70 have no fuel filter? Weird.
Also just to note, the battery is new. Made a video on that here:
https://youtu.be/sFIW61jRP4k