The verb "上" means "to achieve or reach (a certain quantity or degree)", often followed by an object indicating quality.
It is a mistake to state "上" as a verb in this context. The correct role of "上" here is a "result complement"
[Verb + result complement] is often mistaken as a single verb, for example: 當上, 升上, 爬上
當上局長 = become director
升上經理位置 = promoted to the position of manger
爬上主角地位 = climb to the lead actor role
當(v - serve) + 上(result complement - to be) + 局長 (object - director)
升(v- rise) + 上(result complement - reach) + 經理位置 (object - position of manger)
爬(v- climb) + 上(result complement - reach) +主角地位 (object - role of lead actor )
As for 上 being a verb, that include:
1.(v) go up; ascend; get on
2.(v) go to; leave for (a place)
3.(v) be as many as; be up to; reach * (This dictionary made an error here. For example: "上千人" means "over/ up to/ reach a thousand people" and the "上" here is a preposition, used as a function word to indicate a limit or boundary)
4.(v) appear on stage; enter the field * (This definition is redundant, because 上台 (appear on stage) and 上場 (enter the field) mean "go up to the stage" and "get on to the field". both meanings are under definition (1). )
5.(v) fit; install; apply; put on
6.(v) screw; tighten; twist; wind
7.(v) (mahjong) chow; call to create a run/sequence
Text books and dictionaries sometimes, although rarely, do make mistakes from time to time.