How to fix steering slop?

yup
agree
the obvious adjustment (screw and locknut visible from above) is about mesh between the teeth on the sector and the teeth on the ballnut/hydraulic piston that runs up and down the worm screw as you turn the wheel.

however the worm screw that the steering column connects to sits clamped between bearings held in a race at the bottom of the box and a race in the screw in top plug of the box
this screw in top plug is locked in position with a big threaded hex shaped ring

it is not outwith the realms of possibility for this ring to be hit and loosened by road debris
and from that point on the top of the box works loose. this allows the worm screw to move up and down instead of making the ballnut piston go up and down and hence your steering wheel input results in no road wheel output.

undo hex ring 1 turn tap the top of the box round gently until it stops do up hex ring again and ding it tight with your socket extension and a hammer. each corner of the hex has a cut out ideal for being dinged in this way.. :)

the is NOT the correct way to fix the issue. you are supposed to set the preload on these bearings off the car

however as long as the bearing cages have not broken (these look like crank bearings off a sturmey archer bike crank (Raleigh/schwinn)) and the bearings are still in the right place trapped between the race contour on the worm shaft and the press fit bearing races in the box and screw in top plug, all will be well.... or at least better.

if its as bad as you say..... i'd suggest nothing to lose in trying

the screw in plug is like a massive version of the headset fork bearing clamping caps on a 1960s cycle.

Dave