Minor (and Python), but I personally find this to be a little confusing:

if (value := board[row][col]) == empty_value:
    continue
r = f'0{row}{value}'
c = f'1{col}{value}'
b = f'2{row // b_size}{col // b_size}{value}'

You're using an assignment expression to assign a value, but then only use it in the false case. I think this would be much cleaner by using a plain-old assignment statement:

value = board[row][col]
if value == empty_value:
    continue
r = f'0{row}{value}'
c = f'1{col}{value}'
b = f'2{row // b_size}{col // b_size}{value}'

I don't think the line saved is worth burying the creation of a variable.

Minor (and Python), but I personally find this to be a little confusing:

if (value := board[row][col]) == empty_value:
    continue
r = f'0{row}{value}'
c = f'1{col}{value}'
b = f'2{row // b_size}{col // b_size}{value}'

You're using an assignment expression to assign a value, but then only use it in the false case. I think this would be much cleaner by using a plain-old assignment statement:

value = board[row][col]
if value == empty_value:
    continue
r = f'0{row}{value}'
c = f'1{col}{value}'
b = f'2{row // b_size}{col // b_size}{value}'

I don't think the line saved is worth burying the creation of a variable.