If you're having a drought, I'd say you'll be fine using it for a short period of time.
You mentioned adding salt; this will build up in containers every day you use it, and eventually will harm the plant.
Don't use for prolonged periods, and dilute it if possible, as far as possible.
Pasta water contains residue full of carbohydrates, so the bacterial activity in the soil will benefit, but it may cause a layer on top of the soil.
Also, be sure the water was well strained, because it's not best to leave pieces of pasta in the plants' pots.
The fact that the plants are edibles shouldn't be a problem.
The pasta water is non-toxic to humans, so safe to use on edibles.
gardening.stackexchange.com/users/419/J. Musser
I wouldn't recommend it long term but in the short term, it should be fine
EXCEPT it's salted.
Cook your pasta without salt while there's a drought and then use the water.
It doesn't really need salt to cook anyway, usually any kind of sauce you're using on the pasta is salted, so its not essential.
If you notice a difference in the pasta, return to using salt when the drought is over.
Best used on open ground rather than pots, but won't do any harm in pots in the short term (minus the salt).
I'm intrigued that you use salt at all when you cook pasta, frankly, I never do.
gardening.stackexchange.com/users/1380/Bamboo
If you're like me, and use some vegetable oil in the water to keep the noodles from sticking together, you'll want to be careful not to get it on the plant itself.
The oil will heat up in the sun and burn the plant.
As for the soil, as long as there is good drainage, I think you should be fine.
I might consider not doing so if it's in a container.
I'm not sure what effects the oil might have if it sits around the roots, but I would imagine it would suffocate them if it was allowed to collect.
gardening.stackexchange.com/users/2984/The Flash
oil and salt in it might indeed be an issue if you are using just this water and in a container or a place where the drainage is poor.
I would not do it personally.
Also, the gain is low considering that you will need to make a pot dirty to gather the water and let it cool down, the water you saved is lost when washing that pot...
gardening.stackexchange.com/users/7110/Memes
The other answers give good advice, but nobody is mentioning the one fatal error that could be lurking unnoticed: make sure the water has had time to cool before pouring it on .
While you might have thought of this, new gardeners might not.
gardening.stackexchange.com/users/11133/omannay
The water is not lost when washing pot because if it's not salted and no oil is used, its fine to water non-potted plants with it, and therefore the water from the pot is re-used and the pot is just washed, versus if water was not re-used it would be wasted along with water to wash pot.
gardening.stackexchange.com/users/11195/Carron
We are having a drought in California, so I'm just wondering if I could reuse salted pasta water (after it cools) to keep the plants hydrated. Is this a good idea?
Is it okay to use left-over pasta water to water plants, including edibles?
gardening.stackexchange.com
<watering><containers><greywater>
gardening.stackexchange.com/questions/13949
gardening.stackexchange.com/users/7055/Becky
You could use it for a short period of time and dilute if possible. The carbohydrates might even benefit the soil. Pasta water is non-toxic to humans, so safe to use on edible plants.  Pasta water contains residue full of carbohydrates, so the bacterial activity in the soil will benefit. Don't use for prolonged periods, and dilute it if possible and obviously allow to cool first.
Don't use for prolonged periods, and dilute it if possible.    Pasta water contains residue full of carbohydrates, so the bacterial activity in the soil will benefit. Pasta water is non-toxic to humans, so safe to use on edible plants. Make sure the water has had time to cool before pouring it on .