From Scott Sumner,
As you can see the employment ratio was about the same in 2007 as in 1990, and hence the aggregate data shows no evidence that either trade or automation reduced employment during the period studied by Autor, Card and Hanson, as well as Acemoglu and Restrepo.
The above was in response to a paper showing that local unemployment often results from deployment of robots. The same is seen as a result of automation and trade, which is why he includes the last sentence above. Local markets are affected by these structural changes, but not necessarily aggregate employment.
Paul Krugman has done a little digging into the effects of trade on manufacturing employment in the U.S. Overall, he concludes that,
How much of a role did trade play in the long-term decline in the manufacturing share of total employment, which fell from around a quarter of the work force in 1970 to 9 percent in 2015? The answer is, something, but not much.