Start with permission to use the transcript
Before any automation, confirm that the meeting was transcribed with appropriate notice under the firm's policies and the client's agreement. Some clients prohibit recording; some matters are too sensitive to process outside a narrow set of systems. The workflow should check a matter-level flag and skip meetings where processing is not allowed.
Access is also controlled by the platform. Microsoft's documentation for the Graph API to get a meeting transcript lists OnlineMeetingTranscript.Read.All as the least-privileged delegated permission for online meetings, states that application access requires tenant administrators to create an application access policy granted to a user, and describes tenant administrator settings that govern transcript access. I would use the narrowest arrangement that fits, and agree it with the firm's IT administrator rather than requesting broad permissions to make development easier.