it's been pretty hot, and that will cause internode stretch. Also, excessive Phosphorus fertilization can cause longer internodes. What potting medium and fertilizer are you using?

Personally, I wouldn't worry about it too much. As long as you grow it well, it will fill in. You can always pinch it to encourage side growth.

Thank you for your response, nil13; I appreciate it!

I potted the plant in a MIRACLE-GRO type potting soil, and the properties from the label are attached as a photo in case it tells you anything.

I haven't added any fertilizer; I figured the crazy stuff they put in this potting mix should be fine for the time being (is that a safe assumption?).

You're going to want to get some fert with ALL required nutrients (both NPK and the micronutrients/trace elements) in there well before the big spring growth spurt.

Usually with Jasmine you do need to transfer often anyway. With the vine form, not sure? Anyway a point will come where it is root bound, and that will happen before the soil breaks down. The soil should last 2-3 years. Change soil when you repot. After a while you may not have enough room for a bigger pot, and instead can trim the roots down, repot with new soil. You will need to fertilize after 6 months. I prefer to add my own micronutrients with say a kelp powder or liquid, or azomite or both.. I have found it more effective to use various products to ensure proper nutrition. These additives never really hurt anything if not needed. They can be added to water. All potting soils these days are soilless mixes. Even the 5-1-1 mix is going to breakdown with time. Using a more mineral soil that will not breakdown is an option, but I prefer to use the soilless mixes and just maintain them with fresh soil at repotting. You might want to try Happy Frog or
Fafard. I found these potting mixes far superior to Miracle Grow.
As far as more leaves, that may come with time. If not you may try adding another plant, or a different jasmine. Many fragrant types exist that might work better.

So I went down and looked at my potted one. It has internode lengths that are about the same as yours. It's growing well. I wouldn't worry about it. It will fill in. Sometimes commercially grown plants will be grown with very little Phosphorus in order to keep the plant very compact because people like tight plants. Also space costs money and small tight plants are easier to handle.

I have my perennial potted plants in gritty mix so that I don't have to worry about structural failure anytime soon.