Stipule: "an outgrowth typically borne on both sides (sometimes on just one side) of the base of a leafstalk (the petiole). Stipules are considered part of the anatomy of the leaf ..."
If you like order, stipule classification is for you! There are types based on many different characteristics, such as duration, shape, size, position, modification, and more. I preferred the summary of function: "Stipules have various functions. Some stipules are not well understood or may be vestigial." This is the way I feel about many things these days.
This hawthorn has foliaceous stipules, i.e., similar to leaves. Being green, perhaps they contribute to photosynthesis—the business of making energy for the tree. I would guess Spike could use the help, having recently recovered from near death. And maybe this is why stipules are more prominent on the suckers (the next topic).
The Wikipedia article about Plant Development is more open-minded (see Adventitious structures; Buds and shoots). "Adventitious buds [buds that develop in unusual locations on the plant] are often formed after the stem is wounded or pruned. The adventitious buds help to replace lost branches." I agree! Adventitious shoots are very helpful in this situation.