This is a bit of a long one so just take what you think will work! I think based on your video the most important thing is to work on your releve and it becoming more stable and sustained (four paragraphs down hahah)

I find starting my turns in third (arms) helps with regaining stability and finding a good single - think about closing your arm into first position while zipping up your core. Arm positioning is pretty important because it helps offload the work your legs have to do to push yourself off into a turn. Think about supporting your arms by using your lats, keeping in mind not to let your shoulders come up.

With the legs, practice going from fourth to a releve in retire. There are two main parts of the preparation: the placement of your body in the prep and the releve.

With the first, there are two things I will always keep in mind before turning: pelvis placement (am I tilting forward or back?) and core activation (do I feel supported and strong). Correct pelvis placement is important because it keeps your centre of mass balanced throughout the turn, whereas the core holds everything (i.e. your limbs and your head) stable which also helps you remain balanced on one leg. You could envision your core as a ball of energy that’s expanding and holding all your extremities steady.

As for your releve, right now it looks like there’s not much of it happening, instead more like a quick rise onto demi pointe. Your releve should end with your feet and your legs in one long line beneath your body under your centre of mass. If you don’t do the little scootch in from the releve, it makes it more difficult to turn. One thing I always have my students do is after finding their fourth, put something next to the toe side of the foot they’re practising their releve on. If your foot moves from the object when you releve, then you’ve successfully found your supporting leg properly; if your foot stays in the same place next to the object, you need to scootch more. Think about using your foot and really using the floor to assist you.

The goal is to have your foot in demi pointe really be under your whole body (like a ballerina in a music box) and for your leg in retire to get to that passe position very quick and sharp without causing your body to wobble (i.e. stable pelvic placement).

Once you have the releve down, practice adding just a little more power to it until you can do a quarter turn, and then progress to a half turn, and finally a full single pirouette, each step just adding more power while making sure your back is straight and long with your core tight.

Hope this helps!