I would probably have built only one warrior, and possibly a barracks too, and tried if possible to finish both with overflow rolling into the settler.
Growing to pop4 is possible, even the unimproved rice is nice and growth to pop4 should be fast with two wet corns.
That way you can improve rice first and perhaps still have time enough to finish the road...?
Delaying rice for roads is quite costly, sure you gain one turn with the settlement, but you miss out on 6-7 turns of rice production which isn't exacly peanuts.
So I was a bit bored and went ahead and plotted out the micro.
(TLDR: Road first and settler now is stronger than growth and farm)
Road and settler now:
t22 put 1t into road on plains tile 1N of capital.
t23-24 road corn
t25 move to forest 1W of corn
t26-27 road
t28 move to forest 1S of capital
t29,30,31,32,33 farm rice (rice farm can be worked t33)
Settler finishes eot 28. Moves to city site t29 and settles t30 and takes 1 corn from capital.
Capital works both corn and lake on t29 while starting a worker. 14 hammers + 4 overflow from settler.
t30 swap corn for rice. 10 food-hammers t30,31 and 32 means worker is 48/60 at start of t33 when the rice completes.
t33 put 12 food-hammers into worker to complete it.
Start barracks and grow to 4 (end of turn 35 after slavery revolt). T36 start worker at size 4, t37 whip worker taking overflow into another worker. 1st chop completes t38/39 depending on when BW completes, so it will be a 2-3 turn worker.
Grow expansion city to size 2 (end of t33) and swap to worker. 1 pop whip as soon as possible (t38 I think?)
Techwise, its currently 4t to mining and 12 turns to bronze (the 15 turn estimate in the science advisor doesn't include the 20% pre-req
bonus for mining as mining research hasn't finished yet

) at the current 12 bpt.
Four commerce are added on T30 when the expansion city gets founded (1 from new city tile, 1 for the two trade routes and one from the capital swapping to rice). The new city will add 1-2 gpt in maintenance costs so 1t of 0% science will be needed on t29 to pay for the rest of bronze.
The extra commerce will shave 2-3 turns off bronze so bronze should be in by t34-35, which works out well for the first worker to finish the rice farm and move to a forest to start chopping.
Farm and size 4:
There'e 6 food in the box so the capital can be size 4 eot 22 and can start the settler on t23. So put 12 (adjusted) hammers into a barracks and then start settler. 2 corn, lake and bare rice give 14 food-hammers per turn and 13 commerce per turn.
T22 worker moves to capital. T23 worker moves 1S of capital. t24 start farm. Farm complets on t28.
Capital is at 65/100 on t28 and puts 16 food-hammers per turn into settler t28 and 29, finishing the settler with 7 hammers overflow at eot 29.
t30 settler moves to plains forest. t31 to city site. settle t32. Road link completes t35, trade routes established t36.
So farm first gains 7 commerce between t23 and t30 but looses 12 commerce between t30 and 36 as well as 2 turns of growth and production in the expansion city which delays the worker from that city by 2 turns.
Capital starts worker after settler, finished eot 33 and can start straight into a second worker to be whipped after the slavery revolt so capital production is similar though the worker whip may be delayed by a turn due to later BW from lost commerce.
I think the road and settler at 3 is stronger here as it comes out ahead in both commerce and production.