very clear appart from streams which I don't use yet, however you can remove the "else" after the return statement :

        for (int i = 0; i < 3; i++) {
            if (board[i][0] == board[i][1] && board[i][1] == board[i][2] && board[i][0] > 0) return board[i][0];
            if (board[0][i] == board[1][i] && board[1][i] == board[2][i] && board[0][i] > 0) return board[0][i];
            if ((board[1][1] == board[0][0] && board[0][0] == board[2][2] && board[1][1] > 0)
              || board[1][1] == board[2][0] && board[2][0] == board[0][2] && board[1][1] > 0) return board[1][1];
        }
        if (Arrays.stream(board).flatMapToInt(Arrays::stream).anyMatch(n -> n == 0)) return -1;
        return 0;
  }

dude I never thought of importing java.lang.Object

The Integer class already converts decimal to hex string. However if it didn't, I suggest you use switch(decimalDigit)

Now that multiplyDigits method is nice, I used to make a char[] and loop it...
Here is your compacted code :

		return(n>9)?persistence(multiplyDigits(n))+1:0;
	}
  public static long multiplyDigits(long n) {
    return (n>9)?n%10*multiplyDigits(n/10):n;
  }```

Completely forgot you could multiply i in a for loop, this is the upgraded version of mine