Labour productivity, today, is a very hard metric to understand. I'm not sure it means anything as an aggregate.
The ideal/goal of industrial policy (mostly determined in trade agreements) forthe last 40+ years has been... I think Apple is the cleanest, best understood example.
Apple US (or Ireland) houses the engineering. The marketing. It's where the "creativity" lives. It's where the intellectual property is. Where the "platform strategy" takes place. Where "network effects live."
Foxconn (taiwan+china) is where the hard capital investments live. It's where the factories are. Where the workers are.
United States (apple) gets most of the profit. They get most of the market returns (see apple share price, Vs foxcon/etc.). Most of the taxable corporate income. The lion's share of high paying jobs.
China (via foxconn/etc.) gets jobs. Industrial development. Labour productivity... all the benefits of manufacturing.
That was the deal. It was (and still is) what the US and China wanted. They both liked the deal. It worked well. Both governments got what they expected and more.
Apple (and others) did very well. Insane profit margins, market caps... financial returns beyond all expectation. What they wanted.
China did get lots of jobs, industrialised their economy, developed whole regions. They also got what they wanted... in spades.
This had had consequences though.
Instead of modernising manufacturing and continuing to get real productivity gains... Manufacturing got to go backwards. More labour intensive options work again. Fewer capital intensive, high productivity options, were necessary.
That game is kind of played out, but we did not go down the path of manufacturing efficiency. Trying to design the factories of the 2030s now... inevitably speculative work. Risky. Hard.
Meanwhile, the market is used to factories/manufacturing representing the low risk, low margin part of the economy. The proverbial "commodity" business.
Adding innovation, risk to big chunky investments for tight margins... you can see why US (especially the financiers) wanted out of this game originally.
Meanwhile, 1950s manufacturing-based suburban lifestyles... that mind's eye ideal is... Hard to know where reality relates to this now or in the future.