Do streaks negate/ignore the terrain associated defensive bonuses in the scenario?

No.

Streaks do not ignore terrain. They never have and never will.
Streaks only ignore all effects on the Line of Fire.

The defense bonus in "Trouble in Paradise" has nothing to do with the line of fire, so Streaks won't help.

I would think no. Look at this example for the Streaks SE:

Vehicle A has the Camouflage SE, and is in hindering. (DV 20+1+2)
Mech B has Streaks SE. According to my understanding of Streaks, the Camouflage bonus applies, but the hindering does not. So Vehicle A has a DV of 22(20+2).

For this scenario:
At the beginning of each player’s turn, that player rolls one six-sided die. On a result of 1–5, during that player’s turn all units not occupying a sinkhole get +2 to their defense values against ranged combat attacks and all units occupying a sinkhole get +3 to their defense values against ranged combat attacks. On a result of 6, during that player’s turn a strong aurora borealis flare occurs and all units occupying a sinkhole get +1 to their defense values against ranged combat attacks.

It's a special modifier IMO, so no, streaks do not negate the defensive bonuses.

And along those lines it says in the scenario that the sinkholes are not treated as blocking terrain so you would not need streaks or indirect to fire at units in them.