Azor's paradox resonator
The ability would just copy once, and you would end up with a total of 3 filibuster counters after both upkeeps.

Paradox Haze gives you a second upkeep step. That just literally means that after one upkeep, another one happens. At the start of each of those 2 upkeep steps, Azor's ability will trigger, go on the stack, and resolve.

You activate Strionic Resonator during the first upkeep step or the second; either way there will be 1 copy of Azor's ability on the stack at that time, which you can target and copy.

To copy both of them for a total of 4 counters, you would need to also untap Strionic so you can use it a second time (or have another Strionic).