they do look quite a bit stringy, what type of lighting are they getting? i myself bought just a cheapo desk lamp, and an aquarium full spectrum CFL bulb and leave it on for them most of the day to supplement what sunlight they are getting, and that is keeping them pretty normal height.
Yeah, leggy, but in the photos they were "not dead yet".
Get 'em outside,into the soil, ASA practical. They aren't house plants. Beans are more often direct-sowed than transplanted.
Get them twice or three times the light intensity (like, outside, even if they are in a cold frame or poly tunnel). If they can't go outside, they NEED more light.
If they can't go outside, they need out of that flat and into bigger pots ASAP.
How many days did it take to go from soaking them to this point?
If these can't go outside right away, maybe start over and then plant them out into the warmish soil they need before they become so leggy.
Or, if you don't have voracious birds, insects, slugs, mold, fungus, cold wet clay soil and squirrels, direct-sow some outside and some inside, to see how much easier it is to direct sow beans.
Generally, if it is POSSIBLE to direct-sow, it is so much easier that it's better.
P.S. You're smart to start learning indoors with easy, inexpensive seeds. Too smart to do what I did, and kill EVERY SINGLE SEED in three trays, with fairly expensive seeds.
It looks like you have learned NOT to over-water, and to avoid damping off.
You're also learning that they NEED lots of light, and can't stay in the seeding flat very long.
Probably also that there is some fancy planning need to get each kind of seed out from under your limited space that is well-lit, and into the soil on a tight time schedule.
Although I do "know" those five truths well enough to speak them, I've only learned 1 1/2 of those things well enough to DO them right.
I still over-water (but I found a way to make my seedling mix drain SO WELL that over-watering doesn't hurt them). I add a lot of small screened pine bark nuggets to a good quality seedling mix like Pro-Mix, Black Gold or Sunshine.
Also, I keep a cotton flannel pad under the seeding tray so I can bottom-water very uniformly and sparsely, when I'm not succumbing to temptation and over-watering like a maniac.
I have defeated damping off! I make sure that the surface stays dry even when i top-water by covering the surface with larger pine bark chips.
I know they NEED lots of light, and I have around 80% as much as they need.
I know they NEED to get out of the tiny cells ASAP, but I don;t have room for as many 4" pots as I have 72-cell trays.
I need to plan better, but lately that has worked out to not planting them too early, by missing the whole spring season.
Beans are a warm weather crop, that grows really fast...I've never heard of a recommendation to start them in doors. I always direct seed mine when the weather is warmer. They can withstand the heat much better then the cold. You can transplant those but you have an awful lot which equals a lot of work, and they may not make it. You may want to try direct seeding some when the soil temps warm up. The optimal soil temp for germination is 77* and they aren't frost hardy. In my area the earliest time to sow the seeds is beginning of April.