If it was not sown intentionally, then it might be a hitchhiking seed. The seeds are small enough and can stay alive along time in compost. Sometimes in tropical potting medium. In my place, it is not rare to accidentally have them in pots, when you bought a potted plant from exotic plant nurseries. I suspect you grow some tropical indoor, Is that a Nepenthes at the back?
The seedling can stay small for years and years if the condition is not ideal. even in my tropical area. and they do get slightly woody when old, but not truly woody.
And No that is not a Nectarines (Prunus persica)
Some Prunus including P. persica also have leave's gland (Extra floral nectaries), but their morfology, number and position are different, It could be absent, or multiple, on petioles or at the basal of leave's blade edges.
The stipules in Prunus are of different form, they are free, and almost looks like a tiny slim leaves with serrated margin.
The leaves venation in Prunus are also different. Prunus venation are "simple pinnate", with the veins do not clearly "looping", rather they dissapear to the edges (Craspedodromous), or with faint looping (Semicraspedodromous). In the mistery plant; it clearly "Looping" (Brochidodromous).
The margin of Prunus leaves blades are serrated, or sometime doubly serrated. While in mystery plant it is smooth (entire) or dentate with only few teeth.
Below how Nectarines ( Prunus persica looks like)
and the additional annotation of mystery plant
The identification on plant morphology might be confusing with lots of terminology, but it really does help when you get use to it. and it some-kind of fun seeing how amazing the nature is. it is not random at all