The potted trees in nurseries always look perfectly healthy. What do nurseries generally give their trees to keep them that way? Let's narrow down the question and focus on plum trees as an example as I understand that each tree variety might have different requirements.
Bear in mind that many commercial outlets do not actually grow trees in pots, they simply buy them in from a specialist supplier. The actual supplier will raise the saplings under controlled conditions (temperature, light, potting medium) usually under cover, and pesticide/fungicide treatments will be relentlessly used, many of which are not even available to the average gardener. Which is why you're told not to eat the lemons present on a tree when you buy it, so it's not so much how they fertilize that counts, it's those controlled conditions and use of chemicals. Once the trees are hardened, they're sold on to commercial outlets - from then on, they're at risk of picking up the usual diseases and infestations, so any outlet wants to shift them as quickly as possible, before anything gets to the trees, otherwise they're having to monitor and care for them properly over time. In practice, if they have the trees in pots for too long, they dispose of them rather than spending money on the costly upkeep (spraying, feeding, potting on).
I'm pretty sure they don't give them anything initially, although if the tree does not sell within a few months, I imagine they would give them slow release fertiliser appropriate to the plant - something with equal N-P-K values is, I believe, good for stone fruit.
Note that as far as the health of the tree goes, its also that they have been planted in soil with known and ideal properties
(Note: I have no insider knowledge here, just observations while shopping for fruit trees recently, and also because "The Big Tree Company" near us sells slow release fertiliser like I see in their trees at the end of the season. I also know that the instruction for my trees did not require they be fertilised when they are first planted, almost certainly because of nutrients in the soil )