Ann: Extension of Voluntary Suspension, page-181

You can be right.
Anything is possible and I certainly don't know the answer.

But if it's just "continuous disclosure obligations in relation to the technical update re imec & HGST", why a suspension of trading and two extensions ?

And
The statement to the market advising of a voluntary suspension will clearly indicate that it has been put in place at the entity’s request and set out the reason for the request.

And Guidance Notice 16 clearly says that the reason for suspension must be in the statement to the market.

https://www.asx.com.au/documents/rules/gn16_trading_halts.pdf
"The statement to the market advising of a voluntary suspension will clearly indicate that it has been put in place at the entity’s request and set out the reason for the request."

Why is there no reason for the suspension and why ASX agreed with that ?

This seems to be a very unusual situation.

If it is a suspension for an update, why did they not wait to have all agreements settled with Imec and HGST before announcing a technical update to the market ?

There were absolutely no hurry to make this announcement that came out of the blue.
Plenty of time to have the three partners in agreement with the wording.

So why this is not the case ?
A conflict between partners ? 4DS trying to force a disclosure ?

Imo the technical update delay is just something to hide another event.
And ASX and ASIC will probably not object if its a takeover.

ASIC has still to present one single case of totally forbidding a takeover.
ask for some change, declare unacceptable circumstances (TakeOver Panel), yes.
But a takeover is always thought to be in the best interest of shareholders and company.
Takeover will always take precedence on other issues.

Happy to be proved wrong, though.