I have created a Flow by using the "Formula Evaluates to True (New)" entry criteria option but the ant migration tool is not pulling formula conditions when I try to deploy this flow to another sandbox. Flow is not showing any entry criteria in the target sandbox after the deployment.
You are executing your metadata retrieval on an old API version that does not provide this new construct. Update your API version to 55.0.
The Ant Migration Tool is obsolete for the vast majority of use cases. While it's not the source of your specific problem, consider migrating to the
sfdx CLI, which supports OAuth and a variety of other nice features.