...the fee is often taken from the winnings after the game is over, so in no case it can affect the odds and thus be a house edge in the conventional sense of the word (as the casino advantage over the player)
I think you are right and fees or to be honest rake collected by poker rooms doesn't affect the odds, so there is no way for the house edge in the conventional sense.
Every poker room will be happy if you will be winning all the time because they will collect their fees on your winnings so there is no sense for any house edge if they are not playing against you.
In my opinion house edge is only in casino games where you play against the casino and your odds are always lower as theirs and that is why in long run casino always wins but this is not the case with poker rooms and their fees (rake).