Oeh; that's not very well.
From what I can see you have a Sedum album there.
In my country (the Netherlands) they grow outside (as a weed). They survive Dutch rains (750 mm each year) and are very hardy.
I don't know anything about your wetherconditions, but I recommand to place it somewhere outside; not to hot and with enough water.
(if you put some of the leafs in the ground it will start easily again - at least: that happens here)

greets
harry

oh wow, thanks. It was pretty leggy when I got it so I had no idea it was supposed to that dense and compact. We get on average 900mm per year, but this has been the rainiest september in something like 50 years. I'm still reluctant to put it outside because the only place it's safe from the dog is on the roof of the shed where it's fully exposed to the extreme amounts of rain and the wind and honestly it will have next to no sun. Currently it's just living on my windowsill.

Is there another container in that pot that you remove so that the plant can drain when you're watering it? Because sitting in wet soil will probably kill the plant faster than the aphids. If not, find a plastic pot with holes to fit inside the pitcher. Every 8-10 days, remove, water in the sink, drain well, and put back in the pot. It seems determined; you may be able to bring back a healthy plant from the sprouts.

I also tend to "baby" my plants (which I have found is a nicer way to say "kill by drowning" when talking about succulents), but thankfully I've learned to put plants in well-draining mix in pots with lots of holes in the bottom. Keeping them on the windowsills that get hours of sunshine is enough to remedy my "love."

Plus it looks very overpotted - you might look for something that has an inch or two around the root ball for growing.

Thanks for all the help guys :) I know how important drainage is (there are holes drilled out of the bottom of the teapot, although probably not enough)
I'd never heard of overpotting though so I attempted to rectify the issue (and feel free to tell me if this was a terrible idea, I'm open to the criticism) by getting the infuser that came in the teapot (it's about 2 inches across and 2-3 inches deep and made of wire mesh) and opening up the mesh a bit at the bottom by sticking a pen through it to make bigger drainage holes, and then sitting the plant in the infuser and then into the teapot so that I can water it how Danielle suggested. I don't have much available to me in the way of pots right now because I can't drive to pick some up and I pretty much just make do with whatever I can find around the house.

You know, that just may work! I have a mug that has the same type of insert. As contrary as it may sound, the main thing you want to do is keep this plant mostly dry. You can tell if you're keeping it TOO dry if you see the leaves wrinkle a bit, or feel soft. That's plenty of warning to give it a sip of water (a sip! I mean it!). You can always add a little more if it doesn't plump up in a day or so.

If you want to try to get a fuller plant, you can cut the stems halfway and put the cut ends back in the soil after giving them a day to callus over. Bury about an inch or so into the soil. It takes a bit for roots to sprout, and those stems will look worse before they look better, but again, drier soil is better than wetter soil for rooting.

It takes a while to get used to a plant that needs less water instead of more, but when you see them looking better and better the less you water them, you'll embrace it. :)

Thanks :) So is there like an ideal amount of pot space a succulent should have? Most of my plants are in quite deep pots, like I have a graptopetalum paragueyenese in a tin with drainage holes about 15cm deep and 8ish cm diameter. I'm also noticing more and more that my "cacti and succulents" potting mix is less than ideal. I know a lot of people in here mix in things like granite or pumice but I can't seem to find anything in the garden stores around here. I'll keep looking, I suppose.

Yes, everybody is right about the potting and drainage etc. But if it is a Sedum album it will do better outside and have some rough conditions. They don't like pampering like Echies do.
Harry