If an observer block is pushed by a piston at the same time as it is sends a redstone signal, the block it would power after being pushed is stuck in the powered state until it gets a block update. If you build the structure in the first screenshot, and then place a upward facing observer on top of the redstone, the block on the right will stay powered. Also, if you build the structure in the fourth screenshot, the block below won't be powered when the observer updates until you give it a block update.
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Confirmed.. Reason is correct too. When they're updated the moment before they're pushed, they'll stay in powered state 🙂

An extension to this: if you place a sticky piston facing sideways into the input of an Observer and power the piston, the observer block will constantly remain powered, even if you retract it, update it, etc.