Let the $9$ symbols be S, U, D, O, K, !, @, #, and \$.
Because of the repeated U, we need only consider the $4$ diagonal directions and $4(1+2+3+4+3+2+1)=64$ possible placements. Via integer linear programming with a binary decision variable $x_{ijk}$ to indicate whether cell $(i,j)$ contains symbol $k$ and a binary decision variable $y_{ijvw}$ to indicate whether "sudoku" starts in cell $(i,j)$ and goes in direction $(v,w)$, the maximum number of occurrences of "sudoku" is
3.
\begin{matrix} \# &\color{red}S &! &K &$ &@ &D &U &O &\\ $ &D &\color{red}U &\color{blue}S &! &O &K &@ &\# &\\ @ &K &O &\color{red}D &\color{blue}U &\# &S &! &$ &\\ \color{orange}S &@ &K &U &\color{red}O &\color{blue}D &\# &$ &! &\\ ! &\color{orange}U &\# &$ &S &\color{red}K &\color{blue}O &D &@ &\\ O &$ &\color{orange}D &\# &@ &! &\color{red}U &\color{blue}K &S &\\ K &! &$ &\color{orange}O &D &S &@ &\# &\color{blue}U &\\ U &\# &S &@ &\color{orange}K &$ &! &O &D &\\ D &O &@ &! &\# &\color{orange}U &$ &S &K & \end{matrix}
It is clear that no two occurrences can share a U, so even without integer linear programming we have an upper bound of
$\lfloor 9/2 \rfloor = 4$.
By request, here is the SAS code I used:
proc optmodel;
str target = 'SUDOKU';
set SYMBOLS = /S U D O K '!' '@' '#' '$'/;
num n = card(SYMBOLS);
set ROWS = 1..n;
set COLS = 1..n;
set CELLS = ROWS cross COLS;
set DIRECTIONS = {-1,1} cross {-1,1};
set WORDS = {<i,j> in CELLS, <di,dj> in DIRECTIONS: <i+di*(length(target)-1),j+dj*(length(target)-1)> in CELLS};
/* X[i,j,k] = 1 if cell <i,j> contains symbol k; 0 otherwise */
var X {CELLS, SYMBOLS} binary;
/* Y[i,j,di,dj] = 1 if word starts in cell <i,j> in direction <di,dj>; 0 otherwise */
var Y {WORDS} binary;
max NumWords = sum {<i,j,di,dj> in WORDS} Y[i,j,di,dj];
con OneSymbolPerCell {<i,j> in CELLS}:
sum {k in SYMBOLS} X[i,j,k] = 1;
con RowCon {i in ROWS, k in SYMBOLS}:
sum {j in COLS} X[i,j,k] = 1;
con ColCon {j in COLS, k in SYMBOLS}:
sum {i in ROWS} X[i,j,k] = 1;
con BoxCon {ri in 1..n by sqrt(n), rj in 1..n by sqrt(n), k in SYMBOLS}:
sum {i in ri..ri+sqrt(n)-1, j in rj..rj+sqrt(n)-1} X[i,j,k] = 1;
con WordImpliesSymbol {<i,j,di,dj> in WORDS, k in 1..length(target)}:
Y[i,j,di,dj] <= X[i+di*(k-1),j+dj*(k-1),char(target,k)];
solve;
str sol {ROWS, COLS};
for {<i,j> in CELLS} do;
for {k in SYMBOLS: X[i,j,k] > 0.5} do;
sol[i,j] = k;
leave;
end;
end;
print sol;
quit;
If you ignore the extra four symbols and relax all the $=1$ constraints to $\le 1$ so that at most one symbol can appear per cell and each symbol can appear at most once per row/column/box, the maximum turns out to be
still 3.
If you further relax the problem by omitting the $\le 1$ box constraints except for U, the maximum turns out to be
still 3.
If you further relax the problem by omitting all the box constraints, the maximum turns out to be
4.