I'm aware this topic has been discussed ad nauseam. But I'll just throw my observation out there in hopes it will help somebody.

Bottom line up front: fix the oil leaks.

I had the HG, timing chains etc done last February. When I left the garage and for a few weeks, startup had been smooth, every single time.Then a minor oil leak appeared from the engine front, which gradually got worse. Throughout this time, the rattling was getting worse as well.

Being unable to pinpoint the leak myself, I asked the garage to sort it out while they were overhauling the alternator. Which they did. It turned out to be an oil return hose to the crankcase from the PCV. Rattling all of a sudden had almost disappeared!

A few more days later, after a thorough cleaning, I was able to confirm yet another minor leak. This time from the point where the rocker cover meets the upper timing chain cover and the head. I think this one had always been there since February, coexisting with the other leak I had fixed.

A good cleanup and a dab of 300C silicone plugged the tiny pore for good.
Now, 99% of my startups are rattle-free, even after 2200km from last oil change, after long runs and in hot summer afternoons.

My theory is that the rattle is caused by lack of lubrication of the engine's top end as the warm and less viscous oil gradually drains back into the sump. Residual lubricant on the top end, while the engine is stopped, is maintained partly by the two Vanos solenoid check valves, the oil filter canister AND vacuum/pressure within the engine.

A properly sealed engine will maintain the oil at its top end while a leaking one will not. Just as a drinking straw will maintain liquid level while its top is blocked with a fingertip and will automatically drain once the fingertip is removed.

It could be the oil filter itself… when you unscrew the top, you lift the filter from its seat, and then the oil drains down… if the filter is mis-fitted, it might be draining back, in its seated position. A cheap. Fix to just change the filter, and o rings, with care etc. plenty of oil on the seating parts etc….if not, the non return valves behind the vanos solenoids are not that hard to change. But you want to be sure your not going to drop them as they come out. They are not expensive, and only the solenoids are in the way etc.. I did mine whilst doing the chain guides many years back. I had no issues… and 60k more miles, before I sold it, still running sweet.

Agree with everything you wrote. These are all valid points to check while troubleshooting.
Specifically about the oil filter, I find the MAN paper one to be the one that really fits and seats correctly in the canister. I had a no-name one fitted that caused a rattle on every startup. Changed it the following day.