Hello PeriwinklePetals, it is always hard to truly id the plant if the label is gone. But nevertheless, one thing you can definitely improve on, make your media much grittier than it is. I use cacti mix and then top dress my succulents with a combination of pumice and/or chicken grit.
My growing area is different than yours and with our milder winter conditions, it allows me to leave them outdoors even in winter. It is a dilemma at times since we get the much needed rains in winter, and getting the succulents too cold and wet is a death sentence. So to improve on it, I have to make the media as gritty as possible. During late Spring, there is improved growth as the plant adjusts more to the increasing warmth, but it will not like being in our scorching sun as summer starts to come about, so they are positioned in part sun/ part shade area. Thankfully we have city trees that provide shade too as the long and very dry summers marches on. The top dressing then helps cool down the roots too, so it is helps my succulents as well. Echeverias for the most part has shallow root systems.
Looking at your current container, looks okay, hope it has drainage holes. Always empty excess water if any in that saucer. If you do decide to trim down your plant, you may want to use a shallower and wider container though.
I see roots already on the exposed stem portion of your plant, you can trim with the exposed roots intact, and place it in a more appropriate media mix. It should grow much better now, since it is ready to take in water through the roots. Echeverias like lots of light, morning sun is very good, and later in the day dappled afternoon sun. If you intend to bring that plant outdoors later on, try to position it first in part shade so the leaves will not burn. If you intend to just keep it in its current location, it is okay, but do expect the plant to do similar etiolation again, it is seeking much more light.
Just showing here a sample of how my echeveria media typically looks like. Sorry for the extra debris showing there, it is Spring wake up time for the trees so my garden has currently been littered a lot by catkins and leaf kernels.
Good luck on your plants! They still have very good growth potential!