#Java 10, (削除) 262 (削除ここまで)(削除) 260 (削除ここまで)(削除) 248 (削除ここまで) 239 bytes

Java 10, (削除) 262 (削除ここまで)(削除) 260 (削除ここまで)(削除) 248 (削除ここまで) 239 bytes

#Java 8, (削除) 262 (削除ここまで) 260 bytes

v->{int a[][]=new int[7][7],i=7,j,k;for(;i-->0;)for(j=7;j-->0;)a[i][j]=(int)(Math.random()*9+1);String r="";for(;++i<7;r+="\n")for(j=0;j<7;r+=(k=a[i][j])>9|j++%2<1?k+" ":k+" ")if(i%2+j%2>1)for(a[i][j]=k=0;k<9;k++)a[i][j]+=k!=4?a[i+k/3-1][j+k%3-1]:0;return r;}

Explanation:

Try it here.

v->{ // Method with empty unused parameter and String return-type
 int a[][]=new int[7][7], // Integer-matrix with 7x7 zeroes
 i=7,j,k; // Index integers (`i` starting at 7)
 for(;i-->0;) // Loop (1) from 6 down to 0 (inclusive)
 for(j=7;j-->0;)  //  Inner loop (2) from 6 down to 0 (inclusive)
 a[i][j]=(int)(Math.random()*9+1);
 // Fill the current cell with a random 1-9 integer
 // End of inner loop (2) (implicit / single-line body)
  // End of loop (1) (implicit / single-line body)
 String r=""; // Result-String
 for(;++i<7; // Loop (3) from 0 to 7 (exclusive)
 r+="\n") // After every iteration: append a new-line to the result
 for(j=0;j<7; // Inner loop (4) from 0 to 7 (exclusive)
 r+= // After every iteration: append the result-String with:
 (k=a[i][j])>9 // If the current number has 2 digits,
 |j++%2<1? // or it's an even column (indexes 0/2/4/6)
 k+" " // Append the current number + one space
 : // Else:
 k+" ") // Append the current number + two spaces
 if(i%2+j%2>1) // If both indexes `i` and `j` are odd
 for(a[i][j]=k=0; // Reset both the current item and index `k` to 0
 k<9;k++) // Inner loop (5) from 0 to 9 (exlusive)
 a[i][j]+= // Sum the item at that location with:
 k!=4? // If `k` is not 4 (the current item itself)
 a[i+k/3-1][j+k%3-1]
 // Sum it with the numbers surrounding it
 : // Else:
 0; // Leave it the same by adding 0
 // End of inner loop (5) (implicit / single-line body)
 // End of inner loop (4) (implicit / single-line body)
 // End of loop (3) (implicit / single-line body)
 return r; // Return the result-String
} // End of method

#Java 10, (削除) 262 (削除ここまで) (削除) 260 (削除ここまで)(削除) 248 (削除ここまで) 239 bytes

v->{int a[][]=new int[7][7],i=49,j,k;for(;i-->0;)a[i/7][i%7]+=Math.random()*9+1;var r="";for(;++i<7;r+="\n")for(j=0;j<7;r+=(k=a[i][j])>9|j++%2<1?k+" ":k+" ")if(i*j%2>0)for(a[i][j]=k=0;k<9;k++)a[i][j]+=k!=4?a[i+k/3-1][j+k%3-1]:0;return r;}

-12 bytes thanks to @ceilingcat.

Explanation:

Try it here.

v->{ // Method with empty unused parameter and String return-type
 int a[][]=new int[7][7], // Integer-matrix with 7x7 zeroes
 i=49,j,k; // Index integers (`i` starting at 49)
 for(;i-->0;) // Loop `i` in the range (49, 0]:
 a[i/7][j%7]+=Math.random()*9+1;
 // Fill the current cell with a random 1..9 integer
 var r=""; // Result-String, starting empty
 for(;++i<7; // Loop `i` in the range [0, 7):
 r+="\n") // After every iteration: append a new-line to the result
 for(j=0;j<7; // Inner loop `j` in the range [0, 7):
 r+= // After every iteration: append the result-String with:
 (k=a[i][j])>9 // If the current number has 2 digits,
 |j++%2<1? // or it's an even column (indices 0/2/4/6)
 k+" " // Append the current number appended with one space
 : // Else:
 k+" ") // Append the current number appended with two spaces
 if(i*j%2>1) // If both indexes `i` and `j` are odd
 for(a[i][j]=k=0; // Reset both the current item and index `k` to 0
 k<9;k++) // Inner loop `k` in the range [0, 9):
 a[i][j]+= // Sum the item at location `i,j` with:
 k!=4? // If `k` is not 4 (the current item itself)
 a[i+k/3-1][j+k%3-1]
 // Sum it with the numbers surrounding it
 : // Else:
 0; // Leave it the same by adding 0
 return r;} // Return the result-String

#Java 8, 262 bytes

v->{int a[][]=new int[7][7],i=7,j,k;for(;i-->0;)for(j=7;j-->0;)a[i][j]=(int)(Math.random()*9+1);String r="";for(;++i<7;r+="\n")for(j=0;j<7;r+=(k=a[i][j])>9|j++%2<1?k+" ":k+" ")if(i%2>0&j%2>0)for(a[i][j]=k=0;k<9;k++)a[i][j]+=k!=4?a[i+k/3-1][j+k%3-1]:0;return r;}

Try it here.

v->{ // Method with empty unused parameter and String return-type
 int a[][]=new int[7][7], // Integer-matrix with 7x7 zeroes
 i=7,j,k; // Index integers (`i` starting at 7)
 for(;i-->0;) // Loop (1) from 6 down to 0 (inclusive)
 for(j=7;j-->0;) // Inner loop (2) from 6 down to 0 (inclusive)
 a[i][j]=(int)(Math.random()*9+1);
 // Fill the current cell with a random 1-9 integer
 // End of inner loop (2) (implicit / single-line body)
 // End of loop (1) (implicit / single-line body)
 String r=""; // Result-String
 for(;++i<7; // Loop (3) from 0 to 7 (exclusive)
 r+="\n") // After every iteration: append a new-line to the result
 for(j=0;j<7; // Inner loop (4) from 0 to 7 (exclusive)
 r+= // After every iteration: append the result-String with:
 (k=a[i][j])>9 // If the current number has 2 digits,
 |j++%2<1? // or it's an odd column (1st/3rd/5th)
 k+" " // Append the current number + one space
 : // Else:
 k+" ") // Append the current number + two spaces
 if(i%2>0&j%2>0) // If both indexes `i` and `j` are odd
 for(a[i][j]=k=0; // Reset both the current item and index `k` to 0
 k<9;k++) // Inner loop (5) from 0 to 9 (exlusive)
 a[i][j]+= // Sum the item at that location with:
 k!=4? // If `k` is not 4 (the current item itself)
 a[i+k/3-1][j+k%3-1]
 // Sum it with the numbers surrounding it
 : // Else:
 0; // Leave it the same by adding 0
 // End of inner loop (5) (implicit / single-line body)
 // End of inner loop (4) (implicit / single-line body)
 // End of loop (3) (implicit / single-line body)
 return r; // Return the result-String
} // End of method

#Java 8, (削除) 262 (削除ここまで) 260 bytes

v->{int a[][]=new int[7][7],i=7,j,k;for(;i-->0;)for(j=7;j-->0;)a[i][j]=(int)(Math.random()*9+1);String r="";for(;++i<7;r+="\n")for(j=0;j<7;r+=(k=a[i][j])>9|j++%2<1?k+" ":k+" ")if(i%2+j%2>1)for(a[i][j]=k=0;k<9;k++)a[i][j]+=k!=4?a[i+k/3-1][j+k%3-1]:0;return r;}

Try it here.

v->{ // Method with empty unused parameter and String return-type
 int a[][]=new int[7][7], // Integer-matrix with 7x7 zeroes
 i=7,j,k; // Index integers (`i` starting at 7)
 for(;i-->0;) // Loop (1) from 6 down to 0 (inclusive)
 for(j=7;j-->0;) // Inner loop (2) from 6 down to 0 (inclusive)
 a[i][j]=(int)(Math.random()*9+1);
 // Fill the current cell with a random 1-9 integer
 // End of inner loop (2) (implicit / single-line body)
 // End of loop (1) (implicit / single-line body)
 String r=""; // Result-String
 for(;++i<7; // Loop (3) from 0 to 7 (exclusive)
 r+="\n") // After every iteration: append a new-line to the result
 for(j=0;j<7; // Inner loop (4) from 0 to 7 (exclusive)
 r+= // After every iteration: append the result-String with:
 (k=a[i][j])>9 // If the current number has 2 digits,
 |j++%2<1? // or it's an even column (indexes 0/2/4/6)
 k+" " // Append the current number + one space
 : // Else:
 k+" ") // Append the current number + two spaces
 if(i%2+j%2>1) // If both indexes `i` and `j` are odd
 for(a[i][j]=k=0; // Reset both the current item and index `k` to 0
 k<9;k++) // Inner loop (5) from 0 to 9 (exlusive)
 a[i][j]+= // Sum the item at that location with:
 k!=4? // If `k` is not 4 (the current item itself)
 a[i+k/3-1][j+k%3-1]
 // Sum it with the numbers surrounding it
 : // Else:
 0; // Leave it the same by adding 0
 // End of inner loop (5) (implicit / single-line body)
 // End of inner loop (4) (implicit / single-line body)
 // End of loop (3) (implicit / single-line body)
 return r; // Return the result-String
} // End of method