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I understand your concern about the application access from Company A tenant to company B tenant users without the admin permission.
Yes, there is a way to achieve your task Microsoft have a feature to collaborate the external user in the tenant by using B2B collaboration with external guests for your workforce this way external users (company B) can access the resources of company A by using their own credentials to access your company's resources.
In the B2B collaboration once the user is created as guest in your tenant the external user get the invitation to their email and once the external user accepts the invite users can access the applications as per the configuration.
If you would like to ignore the guest invite email to external user, Microsoft have another feature called cross-tenant synchronization it automates creating, updating, and deleting users and allows external users (like those from Company B) to access resources in Company A's tenant without admin approval from their own organization.
Reference: Configure cross-tenant synchronization
Bulk invite B2B collaboration users in Microsoft Entra External ID
Use PowerShell to bulk invite Microsoft Entra B2B collaboration users
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