The Mugi website has some precisions
Descripción Mugi
www.mugi.eus
- The current fares set for each card apply within its specific region, for example: for journeys on the Bilbao tramway with MUGI cards, the BARIK fare applies; for journeys with a MUGI card on the Gasteiz tramway, the BAT fare applies; for Dbus journeys with BARIK or BAT cards the MUGI rate applies.
- Euskotren applies its own fares on journeys that begin and/or end outside a card’s specific region and for inter-region journeys, for example: Hendaia-Bilbao, Eibar-Durango and Deba-Amorebieta
- EuskoTren: On the main Bilbao-Donostia-Hendaia line, MUGI system fares apply only if the journey is between points located between Hendaia and Berriz. If the journey continues beyond those points the Euskotren fare will be applied to the full journey, as it is considered an inter-region journey.
- Bonuses are not applied to the various MUGI/Lurraldebus reduced fare cards (Senior, Disabled, Social & Young) on journeys not included in the MUGI system.
So I take it to mean that a cross-region run on Mugi will cost full paper-ticket price
But even worse for confusion, the Euskotren apps read
Creditrans Barik, General BAT, non personalized Mugi: 1.47€
One-Way tickets: 4.50€

It makes absolutely no sense, Deba is before Berriz in the westbound direction, why is the Mugi fare still applying (if that's what they mean by
the journey continues beyond those points the Euskotren fare will be applied to the full journey, as it is considered an inter-region journey.
)
And as a even more confusing (if it could be), a Barik/BAT card is actually cheaper on dBus (the bus operator for the region of San Sebastian) than a Mugi card of their own region if you someone doesn't want a personalized card.
2026 Fares – Valid on Dbus buses Cash payment of the fare to the driver Standard fare: €1.95 Night fare: €2.65 Cash payment of the tickets doesn´t allow free transfers. Payment by transport card (From April 7th, 2025) NOTE: from January 2025 there is a 40% reduction in transport subscriptions...
dbus.eus
Personalized Lurraldebus and Mugi cards
All groups entitled to a discount will receive a discount when topping up their cards.
The journey brackets are counted within the month. The journey counter is reset to zero on the first day of each month.
- 1 to 20 trips per month: €0.49
- 21 to 50 trips per month: €0.40
- 51 trips or more per month: €0.10
- 51 trips or more per month YOUTH: 0 €
- Night fare: €2.50
Transferable Mugi card
- Day ticket: €0.65
- Night ticket: €2.50
Bat and Barik cards
- Day ticket: €0,49
- Night ticket: €2.50
Incredible for a region designated best ticketing system in the world at the Transport Ticketing Gala (yes, I also discovered today that that exists, I wonder the UK's spot (/s))