I agree with Jung at Heart, but also I believe it should be British registered (SSR) easily done online. You should also hold a ICC (International Certificate of Competence) if you hold an RYA Powerboat 2, the RYA will automatically issue the ICC for a small fee or free if a member. You will need insurance, I use Porthcawl Insurance Consultants Ltd. (insurance-4-boats.co.uk).
We have been going to Spain boating for around 15 years now, excepting Covid. I used to leave my Zodiac down there in storage before Brexit. Always go to Empuriabrava Costa Brava, the biggest Residential marina in Europe. The only time I have to show Docs is in the Marina Office for launching and using the Marina, SSR, Insurance and ICC. Never yet, had to show to any Officials in Spain or on the 'Tunnel'.
Enjoy your trip.
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