I THIRD the opinion. Despite severtal decades of attempted harmonization, the EU is still a "pipe organ" of 27 individual postal and parcel delivery systems. Shipping anything, especially luggage across national borders, should be avoided. Even shipping from Portugal to Spain is fraught with delays and problems.
However, once you are in Spain, sending a suitcase from the local Correos (post office) is easy and relatively cheap. The Correos will provide tracking information too.
IMHO, the Express Bourricot solution is the "best" one, albeit the mnost expensive. They can take the suitcase at Biarritz Airport and deliver it to secure storage at Santiago. It may go via Saint Jean Pied de Port, but it will likely arrive at Santiago well before you do. You pick it up there when you arrive, whenever that is.
The trick here is to be able to be flexible with their shipping routes and patterns. But they do make runs from SJPdP to and from Biarritz, as needed.
They also make more regular runs to transport luggage from SJPdP to Santiago. Contact them at:
https://www.expressbourricot.com/ for more information. Consider than, at this time of year, they may not be working every day - be patient.
The best best thing is to take a train across the border to Irun - Spain. Go to the local Correos there and ship the suitcase to Ivar at Santiago. He will receive and store the suitcase or whatever else you send to him, securely, until you arrive to fetch it.
Over the years, I have done it both ways. I have even used one country's postal system to ship parcels ahead to Santiago. My experience was not good. Thus, I recommend either of the two processes I described above.
Hope this helps,
Tom