I planted some everlasting sweet pea seedlings and they're about 4 or 5 inches tall now

They do have deeply delving roots, as anyone who has ever tried to remove a plant will tell you. I would be inclined to re-pot them in long toms. ie the kind of pot in which Clematis are sold.

I agree they need to go into larger pots and then into the ground. I'd be tempted to put pea sticks in to help support them for when they do start climbing.

Thank you so much! Is it normal for the leaves to be curling a little when they droop like that? I'm a beginner so I'm just concerned that something's wrong. They seem healthy otherwise and i'm trying to harden them off so that I can put them outside as soon as possible.

The leaf curling is to conserve moisture, so possibly they need more water, which is what they would get in deeper pots with more soil for the roots to work through.

I have known two everlasting sweet pea hedges on allotments.
The plants were in the ground. They thrived and produced strong plants with no supports at all.
The weather was not so dry and hot those summers long
ago.

Hot and dry? cool and wet here!

It gets hot here, but quite humid as well. They've been raised inside though, i've only just started the process of hardening them off so that I can plant them out into their permanent place asap...fingers crossed that they'll be happier when they're planted in something that's much deeper lol. Thanks everyone for your help. Does anyone know how tall or how many sets of leaves they should have before I transplant them? I just wanna make sure i'm not doing it too early :)

Just a thought, but have you pinched out the growing tip so that it'll produce side shoots and a bushier plant to plant in its final position. I have some in quite shallow its at the moment but each plant has about 4 shoots now. I pinch out back to 4" from the base to get a better plant to plant. I would be interested to find out if your have scent because when I grew them in a previous garden they looked great but had no smell.

I have pinched out the ones that have 3 sets of leaves, but I'm not sure if I should pinch out the ones with 2 leaves, or wait for them grow another set. They're already at least 4 to 5 inches tall so I've been trying to figure that out for the last few days....any advice on that is welcome and appreciated. As for the scent, to my knowledge, the everlasting sweet pea variety has no fragrance, but i'll let you know if i wind up with any pleasant surprises.

Just an update, I took a measurement when I got home today and they're actually around 8 inches tall. Most of them still only have 3 pairs of leaves and I've pinched almost all of them off. Should they have more leaves by now? They've been getting plenty of light so I'm not sure what think at this point

We have had a Gobi Desert wind blowing here all day. I am tired of it. Blows me off balance, have to struggle with a walking stick. It dries plants out. I am struggling to take containers of rainwater from my butt in my Rollator Walking Aid to save them. Glad I have deep plant saucers so it doesnt run away.