Hello waltonftw
The etiolation on your sempervivum doesn't seem too bad, I have often received them looking just like that (or it takes me a few days or even weeks to have time to plant them) or even paler and droopier and they always recover.
To help with the droopy leaves, I would suggest surrounding your semp with small pebbles or gravel, or chicken grit if you can find it. For tiny semps, I use a toothpick or small butter knife to gently lift the leaves and push the stones under them as far as I possibly can. The cactus mix they are in will work well for them, although I would keep the bark pieces away from the trunk or leaves because bark can hold moisture and invite rot. Watering it too often can also cause the leaves to droop like that and just make semps look quite sad! How often are you watering it? I would also drill a few extra drainage holes. Semps need very good drainage and one small hole might not be draining the soil enough to its liking. When you take it out of the pot, see if it is growing small white roots, that's a good sign. As for producing chicks it all depends on what kind it is, some semps produce lots of chicks and often whilst others produce few or rarely offset.
I don't think your semp will do well with an artificial light, I have never tried it but reading through older threads on here it isn't recommended. I live in a very hot climate and my succulents only get morning sun and they thrive. During very hot weather like we are having now I cover them with 50% shade cloth so that even the morning sun doesn't hit them full on. To get yours used to being outside you can try protecting it with a small piece of shade cloth or putting it in dappled light beneath a tree or chair or some other source of shade. I would keep it in very dappled light until it has regained some color and outgrown that sunburn a little bit and then gradually introduce it to full sun over the course of a week or so and see how well it does. Once the temperature gets over 85 mine become visibly stressed and will roast in the sun if I don't move them onto my patio.
I think yours will recover fine, it looks healthy enough to me
