@Artem Shaturskyi, Thanks for posting in Q&A. Based as I know, App Protection Policies are designed to ensure that corporate applications are accessed securely, often requiring the use of Microsoft Edge to maintain compliance and protect data. So disable sign-in redirection to Microsoft Edge after applying App Protection Policies is not directly supported.
From your description, I know you have conditional access policy been configured to require app protection policy and "Require approved client app". Please confirm what we configure under Target resources > Cloud apps? if we change to only include the cloud app we want. will the result be different?
Meanwhile, I notice you have selected "Require approved client app", please check which application the client use to access the cloud resource. Is it under the supported app list in the following link"
For sign in frequently issue, I want to confirm if we set Sign-in frequency in conditional access policy.
In addition, please check sign in log to see if there' s any error we will get when the user accesses the cloud resource.
Please check the above information and if there's any update, feel free to let us know.
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