Is there any way to read Managed Metadata column value in SharePoint using REST API?
You can use TaxCatchAll in REST API to get the Managed Metadata column values .
Refer this article having detailed steps to get metadata column value.
It's possible to retrieve Metadata column values using SharePoint REST API:
And if you want to get the expand properties such as term text, you can use the hidden list field TaxCatchAll.
This field exists for all rows having taxonomy data, and includes all the terms used.
The good thing is that this is a lookup field pointing to the hidden taxonomy list located at [site url]/Lists/TaxonomyHiddenList/AllItems.aspx.
Check this blog to get more details