Never mind, Olly. We all started this way.
This script works for me in an English UI. I commented some lines for your convenience:

#IfWinActive ahk_exe SDLTradosStudio.exe ; this needs to match the info of Spy tool
; WINDOWS + A (change it to your suits)
#a:: ; I wouldn’t use CONTROL+A to trigger any script
    Send !h
    Sleep 100    
    Send b ; (without ALT works as well)
    Sleep 200
    Send {down 2} ; Down x2, as Down x1 is FINALIZE
    Sleep 50
    Send {Enter}
    WinWaitActive, Batch Processing ; Wait for the BATCH PROCESSING window to show

    Send {Shift down} ; SHIFT + TAB x2 (Focus on FINALIZE button)
    Send {Tab 2}
    Send {Shift up}
    Send {Enter} ; FINALIZE button    

    Sleep 5000 ; Waiting the ANALISYS to finish
    Send {Enter} ; CLOSE button
    
    WinWaitActive, Question ; Wait for the QUESTION window to show
    Send {Enter}  ; YES button
Return
#IfWinActive

If the script doesn’t work, you may want to tune the Sleep timers until it works.

The only step not automated is waiting for the analysis to finish. I leave it for you...
:-)
Tip: WinWaitActive function.
Good luck!

There is a problem with your second WinWaitActive, and is that the script doesn't wait because the window Batch tasks is already active. That's the reason you need to press manually the Enter key.

So you need to add an extra requirement with another parameter of the WinWaitActive function. WinTitle parameter is fine, but you need to add something like Finish completed, whatever comes up in the window as soon the task is completed. The documentation of this WinWaitActive function should help you in both batch tasks.

I haven’t tried, but I mean the parameter WinText.

The line should be something like:

WinWaitActive, Batch Processing, Finish task completed

Where Finish task completed should be whatever comes up when the Finish task is completed. If the script doesn’t work, please set the built-in variable A_DetectHiddenText to Off and try again.

Nothing comes up, the task is completed and then you need to click on the Close button. Is the problem that there is no WinText under the Close button that I want activated (clicked) after the batch task has completed (according to winspy)? Also tried with detecthiddentext, off (just inserted the line at the top of the script, right?). By the way, if this is dragging on too long for, please say so!

Olly

I’ve checked a bit this.

If you use Trados Studio 2019, there is not such Finish task completed text. The only text recognised by Spy tool is Restart Preparation and it only appears when the Finish task is done. So this is what you need.

I don’t know what you’ve already tried. but I believe this should work:

DetectHiddenText, Off

WinWaitActive, Batch Processing, Restart Preparation

(Not tested)