New leopard gecko not eating. Also, I'm afraid to leave phoenix worms in the tank

[Malum Argenteum]

Without knowing the temps, it isn't possible to say what is going on exactly with the feeding. An IR temp gun is a necessary piece of equipment for any herp keeper -- any brand and model will work fine (link to example). The temps you mention would be fine starting points for the gecko, and the temp gun enables the keeper both to make sure that those temps continue, and to check how the gecko is using the various temperature regions in the enclosure so that its preferences can be maximized (e.g. if it hangs out on the cool side a lot, turn down the warm side temps gradually until it thermoregulates regularly).

A basking lamp is a bit of an odd way to provide heat to a leo, but it can work. Leos are not basking thermoregulators by nature -- they seek out secluded crevices of the proper temps and moisture levels and stay there, so it is important to make sure that the hide areas it uses are maintaining suitable temps rather than forcing the gecko to seek out unnatural hot spots.

Some thoughts beyond temp concerns: that gecko has been eating well and looks good. No obvious health issues.

Many geckos (IME, after offering them to hundreds of terrestrial geckos) won't eat Phoenix worms. Too bad, since they're among the more nutritious of feeders. Offering crickets, mealworms, superworms, and roaches will allow you to figure out which will work best for you and the gecko. The last three types can be left in the enclosure in an escape-resistant bowl -- I use these, but in looking for a link I learned that there are some nice looking ceramic ones available too. Aside from possible temp issues, the type of feeder being offered is the likely cause of any feeding issues from the gecko in the photo.

Though this isn't relevant to the current feeding concern, all feeder insects offered need to be dusted with a full spectrum supplement at every feeding; Repashy Calcium Plus is my recommendation. Plain calcium is fairly useless since it has no D3, which is necessary for calcium metabolism unless sufficient and metered UVB is provided and the gecko uses it (the bulbs you linked do not provide UVB, and I don't recommend new keepers provide UVB anyway since it is really easy to misuse). Plain calcium also does not provide Vitamin A, which is not present in sufficient amounts in any feeder insect and is necessary for health. Some keepers like to also leave a bowl of plain calcium in the enclosure; I don't, and it isn't necessary.

So: get an IR gun and dial in temps, offer a range of feeders, and get an appropriate supplement are my recommendations. Hope they help.