Working part time in UK as you propose does not necessarily make you a cross border worker in the sense of Moses's link.

Cross border health arrangements survived Brexit virtually unchanged so if you're not performing work in Spain then as a UK PAYE employee you ought to be entitled to a workers S1 issued by HMRC not DWP.

You will be tax resident in Spain with all that implies but because of the Dual Tax Treaty (DTT) will get credit for the PAYE tax you pay in UK.

This link refers to France but also applies to Spain.

https://www.remaininfrance.fr/workersentitledtoans1

Only takes a phone call to HMRC to find out.

Do you have a link for this, please?
I am not doubting it, I thought it might be the case but couldn't find it set down anywhere and I would like to see a text.

Correct, I have an S1 form for my healthcare in Spain as as well as private insurance as I work in the UK and pay Tax and NI in the UK on PAYE. My wages are then subject to the double taxation treaty. My reality is that I pay a very small amount to the Spanish.