Rattling 2k miles after HG replacement.. but only after sitting 5 mins.

2013 Prius. Replaced the HG about 2-3k miles ago @ 142k miles. Everything was kosher, until recently.
When the car sits overnight or more than an hour, no startup rattle.
When I drive the car, turn it off for about 5 mins & turn it back on, engine rattles. Initially thought maybe something in the fuel pump was bad, so I just replaced the entire assembly with an OEM unit - still rattles.

Intake manifold cleaned, EGR circuit cleaned, injectors were sent to be rebuilt / balanced, new plugs (original coils), new gaskets, headstuds, head machined, block was checked for flatness (0.05mm feeler gauge). Engine runs great otherwise. I do about 1500-2000 miles a month at about 90% highway and it runs great. No coolant loss detected.

Two things I still need to do - replace evap solenoid (sticky?) & refresh ECU to the latest firmware per T-SB-0041-15.
I also read one situation on reddit where someone's catch can tubing was too large, so it would sporadically rattle for a few seconds until vacuum was built. Currently sourcing an OEM PCV tube to rule out the possible catch can issue.

Any other suggestions? Sticky EGR valve?

 

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If I start it and immediately drive before the engine starts, I don't really get a rattle. I can't tell if it goes away when I rev it, since the rattle is short and stops within a second. Also, if you're facing the engine, it sounds like the rattle is coming from the right side of the motor where it interfaces with the trans. No CEL.

May be related - when I first changed the HG, I would get a weird half second low idle as shown in this video - which led me to believe the fuel pump assembly needed to be replaced.

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