Hi there, you are though to Dr. Jake. Im a UK based vet. Im sorry to hear of your concerns with your leopard gecko.
the video you have provided is very concerning. Mush is showing classic signs of metabolic bone disease. this is seen in the video where his walking is altered as his bone have become soft and deformed. this occurs due to chronic malnutrition due to a lack of calcium and vitamin d3 in their diet. metabolic bone disease if untreated can lead to soft bone, broken legs which results in their limbs being bent at angles as seen in your video.
if not addressed then the condition can lead to kidney and liver conditions which leads to poor appetite and lethargy.
overall this starts with poor husbandry months earlier from when the condition becomes visable and evident. to prevent metabolic bone disease leopard geckos require a varied live food diet including cricket, locusts, mealworms and waxworms which have been gut loaded- this is where you feed these insects nutritious vegetables and fruit , the nutrients from feeding the live food well will then get into the geckos when they eat the live food. it is important that the livefood is supplemented with vitamin and mineral powder at each feed, this should be a combination of calcium and vitamin d3 .
as well as good diet, i recommend providing ultraviolet lighting to leopard geckos - i provide this to my own geckos and feel they greatly benefit from this to allow for adequate absorption of calcium and vitamin d3 production. the arcadia shade dweller bulbs have been designed for geckos such as leopard geckos
i would recommend making an appointment with a local vet who has experience with reptiles who can help provide you with appropriate medications to possibly treat this and for an assessement of the abdomen to make sure there is no sign of a blockage or impaction which has caused the lack of eating anf lack of faeces. i have to warm you that this looks quite extensive and serious and he may not make a recovery from this condition.
for feeding , you will have to provide oral calcium such as calcivet orally daily which can be purchased online. if your gecko requires assist feeding then emeraid carnivore would be the most appropriate
i hope all this information helps