隣人, 近所, and 町内: neighbors, nearby areas, and neighborhood people
Distinguish the person named by 隣人 from the areas named by 近所 and 町内. Read plant care, a new bakery, park cleaning, and a festival float, including people identified with の人.
隣人: the person receiving a request or coming to greet you
隣人 (りんじん) identifies a neighbor as a person. 「留守中の植木の世話を隣人にお願いした。」 means “I asked a neighbor to care for my plants while I was away.” 隣人に marks the person who received the request. Asking for care does not itself report that the care was completed.
「新しい隣人が焼きたてのパンを持って挨拶に来た。」 means “Our new neighbor came to introduce themselves with freshly baked bread.” Here the neighbor is the person who came with bread. Being a neighbor does not establish a family relationship, an existing friendship, or an exact distance between homes.
近所: a nearby area and a person from that area
近所 (きんじょ) refers to a nearby area. 「近所に新しいパン屋ができました。」 means “A new bakery opened nearby.” 近所に tells you where the bakery opened. Reading 近所 itself as a single neighboring person would confuse a place with a person.
「留守の間、近所の人が花に水をやってくれた。」 means “Our neighbor watered the flowers while we were away.” The whole expression 近所の人 identifies the person. This actual watering and the earlier request to a 隣人 are separate scenes; they should not be merged into one person's sequence of actions.
町内: movement within an area and the people from it
町内 (ちょうない) can identify the neighborhood area. 「祭りの日は町内を小さな山車が巡る。」 means “On the festival day, a small float makes its way around the neighborhood.” 町内を gives the area of movement. The thing traveling around that area is the small festival float.
「日曜日の朝、町内の人たちと公園を掃除した。」 means “On Sunday morning, I cleaned the park with people from the neighborhood.” 町内の人たち names the people taking part. Keep the distinction between a person, an area, and an area's people without supplying an exact distance or an administrative boundary.
In 「近所に新しいパン屋ができました」, does 近所 identify one neighboring person?
Show the answer and why
No. It identifies the nearby area where the bakery opened. People from that area are expressed with wording such as 近所の人, which includes 人.

