So if i decide to put Smaug engaged with me at the start of the quest phase, is that consired optional engagment or not?

I was just wondering this because i played today for a long time this battle of Lake-town quest (still never beated it) and i came up with a situation that if Beregond wouldn't get boost from captain of Gondor, he would get killed. So i played it like he would the one defense boost (but it doesn't matter i lost the game anyway...)

It is not. The only thing which is considered optional engagement is the optional engagement you get to make during the encounter phase according to the core rulebook (or the two optionals if you're using Halbarad). Nothing else counts as optional engagement, even if you are deliberately choosing to trigger an effect to engage an enemy.

Thanks for helping me with this