According to Google Support regarding “What is iOS Account Manager”:
”Do you mean 'iOS Account Manager'? If so, you'll need to seek support from Apple, as that is a system used by Apple to remotely manage devices via a company account. You may have been issued the device by a company or school, where the Admin there can advise you more about these settings.
If you have acquired a device, that already has a 'iOS Account Manager' installed, then you need to ask the provider of the device to remove the management, or to arrange a return and request a refund.” [Source]
Given the vast amount of unanswered and locked questions on the Google Community asking the same question, and the absence of an official statement by Apple on the origin of the application it should be regarded as suspicious.
If you are seeing Google Workspace imagery and references related to InteractiveLogin, ServiceLogin and Google API when logging in or using their services and you do not have a subscription with them then, you should raise this them via their social media account on X/Twitter (as there is no other way to contact them since you probably don’t know who is the Administrator).