Adding metadata to document libraries: custom content type or default Document content type?

Michelle has covered the content type design well. I would add a small governance agreement for the shared columns before publishing Company Document: business definition, allowed values, accountable owner, whether the field is required and how a change is approved. For example, define whether Department means the document author, the business owner or the intended audience. A centrally published column can still collect inconsistent information if that meaning is unclear.
In my published PALO Framework, the data lifecycle and Data Assurance model (https://paloframework.org/docs/palo-data-assurance-control-plane.html) connect ownership, lineage, freshness and permitted purpose to the evidence used for a decision. Applied here, I would pilot the content type in two libraries, classify a sample of existing files and check both completeness and correctness against the document content. Record missing values as unknown rather than filling a convenient default that looks valid. Keep library-specific fields outside the shared core unless there is a common business meaning.
If these libraries will later ground Copilot answers, a completed metadata field should not be treated as proof that the content is current or approved for that use. PALO provides that governance distinction; SharePoint remains responsible for the actual content type, permissions and publishing configuration.