The sfdx CLI has the ability to generate a report of the unit test coverage in JSON format with the default naming convention test-result-codecoverage.

I would like to be able to retrieve this JSON file and push it automatically to the repository on every unit test execution.

As an example please find a possible sfdx command to achieve it: - sfdx force:apex:test:report --testrunid 7075J00001NZBNIQA5 -c -r json -d folderDirectory #testRunID is the value from the ApexTestResult obj AsyncApexJobId field
Please find more information on the official salesforce documentation about it https://developer.salesforce.com/docs/atlas.en-us.sfdx_dev.meta/sfdx_dev/sfdx_dev_testing.htm