A family of Microsoft on-premises document management and storage systems.
AFAIK, SharePoint does not provide true metadata inheritance for standard folders in a Document Library. A folder can have Column default value settings, but those values are applied only to new files created or uploaded directly into that folder. They do not automatically cascade to child folders, nested subfolders, existing items, or files in deeper levels. Similarly, changing a parent folder's metadata does not update its descendants.
There is no setting I'm aware of to enable recursive metadata inheritance. If you require inheritance, Document Sets provide limited support through Shared Columns, allowing files within the Document Set to inherit the parent's metadata. However, this does not extend to nested subfolders.
For multi-level metadata inheritance, you might want to use Power Automate to copy parent metadata to newly created files and folders, or use PnP PowerShell, SharePoint event receivers/webhooks, or Azure Functions. If possible, you could simply consider reducing reliance on deep folder structures and organizing content primarily through metadata and filtered views instead.
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hth
Marcin