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Unfortunately ,This is a known limitation. You cannot programmatically export the ARM template.
The export template feature doesn't support exporting Azure Data Factory resources. To learn about how you can export Data Factory resources, see Copy or clone a data factory in Azure Data Factory.
There are a number of similar requests shared here ADF shall be able to export ARM template by powershell as Ideas and feedback, you can upvote or add one too for official MS response.
You can try Power automate recorder to implement that flow if need be :
https://learn.microsoft.com/en-us/power-automate/desktop-flows/recording-flow