I do have another EU nationality. How does Brexit affect my rights of residence?

If you have another EU member state nationality, you will be able to come to Spain and register on the same conditions as you did before the end of the transition period - and as any other EU-National - even after 31 December 2020. If you were registered as a UK national, you can obtain the new TIE or request a change of nationality shown in your EU residence Certificate, to switch it to your EU nationality.