Von Neumann Neighborhood Your goal is to make a function that takes the coordinates of a cell in 2D space and a distance \$r\$ and returns the coordinates of all cells in the  input coordinate's von Neumann neighborhood of radius \$r\$. That is, all cells at most \$r\$ away in Manhattan distance.
For example, given the following cell coordinates and radius pairs:
[1, 1], 1 -&gt; [0, 1], [1, 0], [1, 1], [1, 2], [2, 1]  
[2, 2], 2 -&gt; [0, 2], [1, 1], [1, 2], [1, 3], [2, 0], [2, 1], [2, 2], [2, 3], [2, 4], [3, 1], [3, 2], [3, 3], [4, 2]

This is what the von Neumann neighborhood looks like:

More information about the von Neumann neighborhood can be found here.
This is code-golf, so shortest amount of bytes wins!
APL (Dyalog Extended), 23 bytes

-4 thanks to ovs.
Anonymous tacit infix function, taking coordinates of a cell and radius as left and right arguments. Requires 0-based indexing.
{⍺∘+¨⍵-⍸⍵≥+/¨|∘.,⍨⍵…-⍵}

Try it online!
{…} &quot;dfn&quot;; left argument is ⍺ and right argument is ⍵:
 ⍵…-⍵ inclusive integer range from radius to negative radius
 ∘.,⍨ Cartesian selfie product
 ⊢m← assign to m and pass that
 | absolute values
 +/¨ sum each (gives matrix of Manhattan distances)
 ⍵≥ indicate which ones are less than or equal to the radius
 ⍸ ɩndices where true
 ⍵- subtract from radius
 ⍺∘+¨ add the cell coordinates to each