You don't need new spokes. Use the existing spokes in place.
Count the spokes so you get a replacement rim with the same spoke hole count. Looks like 36 in the photos.
Most trikes have 24" rims. There are 7 different diameters of 24" rims. Check the tire sidewall for the right size. Most rims don't have the size on them. Tires with a decimal point width are all interchangeable, tires with fractions all have their own special rim size. 24 x 1.nn 24 x 2.nn is the standard mtb size.24 x 1 & 3/4 is the Schwinn size. There are some fractional skinnier sizes. 24 x 1 & 3/8 (S and EA), 24 x 1 & 1/2, 24 x 1 & 1/4, etc. They vary quite a bit in diameter so if you use a different size from oem, you will need new spokes and a new tire. Generally the skinnier the tire, the larger the rim. The overall diameter of the tire on the wheel is pretty close for all of them.
We all know 1 & 3/4" = 1.75 mathmathically but that is not the case for bike tires.
1: put a drop of penetrating oil on each nipple so it goes in the threads. let that soak a while.
2: use masking tape at the last spoke intersection to hold the spokes in relative position.
3: spoke wrench to undo all the nipples. Use a real spoke wrench in the right size so you don't round off the nipples. No crescent wrenches or sheet metal spoke wrenches.
I use a magnetic dish to put the the nipples in. Steel nipples will stay put. Brass won't. Steel nipples rust solid, Brass doesn't. Older bikes mostly have nickel plated brass. Chinese BSOs have steel.
Steel vs aluminum rim. Each model/brand/metal of rim will need a different length spoke. Get a similar profile of steel rim and the current spoke length will be fine. There is several mm of wiggle room on spoke length. Longer nipples get you more threads if the spokes are too short.
If the spokes are a little too long for a particular rim you can grind off a couple mm when the wheel is done so the spokes don't poke holes in the inner tube. If the nipples bottom on the spoke threads before the spokes are under any tension, you will probably break the spokes trying to force them on further.
BTW, one of the spokes is in backwards. The spoke heads should alternate up/down.