Von Neumann Neighborhood
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.
{⍺∘+¨⍵-⍸⍵≥+/¨|∘.,⍨⍵…-⍵}

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{…} &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