In the building of the Pilgrims Office in Santiago is an office of the Galician Tourist board where you can get a credential for your journey to Muxia and Fisterre.
When we got the question at the PO counter, we pointed them tho the Tourist board
People who walk from Santiago to Finisterre or Muxia can qualify for the Fisterriana or Muxiana certificates. These are guest welcome certificates from each town's tourism authorities. They have no standing with the Cathedral in Santiago and are not Compostelas.
The Galicia Tourism Office issues a credencial sort of document for many paths, to support Galician tourism. It's what they do. That they are colocated in the same building as the Cathedral's Pilgrim Office is just a coincidence.
In theory, starting at Muxia, walking to Finisterre, and thence to Santiago is more than 100 km - just. But, it is NOT a currently approved CAMINO route. One cannot just walk ANY100 km into Santiago and call it a Camino - eligible for a Compostela. The route must have been officially approved.
To be an approved Camino route, the route must have documented, historical evidence to support the case for approval. The route must be reviewed, and then approved, by the governmental bodies that oversee this sort of thing. Ultimately, the proposed new Camino route must be approved by the Cathedral authorities.
As regards the unique Irish Camino; historically, pilgrims for distant places would use a boat or ship to travel from Ireland to A Coruña. On making landfall, they would continue their pilgrimage, on foot, to Santiago.
This is the basis for approval of the Irish Camino. A pilgrim walks the first 25+ km in Ireland, then transitions to a boat, making their way to A Coruna by sea or air. At A Coruña, pilgrims transition to walking. This is a well-documented historical route. The 25 km in Ireland and about 75 +in km Spain, add to the 100km required to qualify for the Compostela.
Conversely, the Muxia - Finisterre - Santiago combination - alone - lacks the historical lineage and proof required for consideration as an approved Camino route.
In the past decade or so, IIRC, only three routes have been newly approved: Camino de Invierno (2016), Irish Camino (2018?) and the Spiritual Variant of the Portuguese Camino from Porto to Santiago (2019?)
Hope this helps,
Tom