I was just able to test both faucets and the first one filled the bucket up in 50 seconds and the back one took 2 minutes.
Here’s the sprinkler I’ve been using: Melnor 65074-AMZ XT Turbo Oscillating Sprinkler with 2-Way Adjustment and QuickConnect Product Adapter Set, Amazon Bundle https://www.amazon.com/dp/B07P9FH2FL/ref=cm_sw_r_cp_api_i_6K1W4Y4W3NJG1E8BKD9Z
A solid oscillating sprinkler is the best/cheapest option, in my opinion, for long narrow yards.
I've got one of these and it can go as wide or narrow as you want. The only downside is it needs to be in the middle of where you're watering. This sprinkler costs a little more BUT you could set it up on the corner/edge of the lawn and adjust the size of the rectangle in front of it.
Melnor 65074-AMZ XT Turbo... https://www.amazon.com/dp/B07P9FH2FL?ref=ppx_pop_mob_ap_share
If it's just a square, an oscillating sprinkler is probably your best bet. I have this Melnor that works well for me, and with just 4k sqft, that may cover the whole yard.