Build says "Ready to Submit" after Assigning to External Testers

I am trying to upload an IPA to testflight for external testing groups via a script that uses a combination of xcrun altool and Appstore Connect API endpoints. xcrun command executes successfully, as well as the endpoint to assign the new build to test groups. When I go onto the appstore connect website afterwards, the build is assigned to the correct external groups, but the status of the build stays at "ready to submit", and the testers do not see the new build on their testflight app. This is not the first build of this version, so the review for build 1 has already been completed. These are the steps I use:

xcrun altool --upload-app --type ios -f path_to_IPA -u username -p password

1. I then set a sleep timer for 10 minutes, allowing the app to go from the "Processing" state to the "ready to submit" state.

2. Hit the endpoint to assign this new build to my test groups

curl --location --request POST "https://api.appstoreconnect.apple.com/v1/builds/${BUILDID}/relationships/betaGroups" --header "Authorization: Bearer ${JWT}" --header 'Content-Type: application/json' --data-raw '{
    "data": [
        {
            "id": "group1 id",
            "type": "betaGroups"
        },
        {
            "id": "group2 id",
            "type": "betaGroups"
        },
        {
            "id": "group3 id",
            "type": "betaGroups"
        }
    ]
}'

1. Go to Appstore Connect website, the new build still says "Ready to Submit" despite there being external groups assigned. If I do this entirely through the website, once it processes and says "ready to submit", adding external groups to the build immediately makes it available to them and changes the status to "Testing".

2. If I (through the website) remove a test group and add it back in, the build immediately becomes available to the test groups and a notification is sent out.

There does not appear to be an API endpoint to submit an app for review, so how do I make the build status "Testing" if the external groups are already assigned?