Ok so there is good and bad news.

The good is that one of the keys is now always working, even after a day or 2.
The bad is one of the key coin batteries i recently replaced is now at 1.5v instead of 3.6. So i'm good for another replacement...
I usually switch between both keys each month so they both stay charged. Probably a faulty battery.

That said, i still don't know why the remote / sync completely stopped working for few days.

Removed the plastic trim from the hatch, inspected the EWS FZV amplifier which looked fine, as well as the wires (found a similar post where the power wire of the amplifier snapped in the wiring boot of the hatch)

And yes when you want to sync 2 keys or more, need to put only one in the ignition and then do the buttons procedure for each key one after the other, and fast.

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E53 - 2005 3.0dA