Does your jurisdiction maintain a list of trusted entities to qualify e-signatures?

Yes. Qualified trust service providers can be checked via this link:

https://sede.serviciosmin.gob.es/Prestadores/Paginas/Inicio.aspx

Please provide a quick overview of the law, i.e., types of contracts that qualify for use with e-signature.

eIDAS Regulation establishes the legal framework for the use of e-signatures in all EU territory, including Spain. Law 6/2020 mainly establishes legal standards to be met by qualified trust service providers in Spain. eIDAS Regulation distinguishes three categories of e-signatures depending on their level of security: simple, advanced and qualified. A simple e-signature is the least secure and the qualified one gives the maximum reliability and probative value.

What is the legality of e-signatures in your jurisdiction? Are there key exceptions?

In Spain all 3 categories of e-signatures are used depending on the importance of the document. E-signature shall not be denied legal effect and admissibility as evidence in a litigation procedure solely alleging that it is in an electronic form or that it does not meet the requirements for qualified electronic signatures.
Spanish law 34/2002 grants legal effect to contracts signed with e-signature, regardless of its category.

What is the e-signature law enforceable in your jurisdiction?

EU Regulation nº 910/2014, of July 23, on electronic identification and trust services for electronic transactions in the internal market (“eIDAS Regulation”) is the main law on e-signatures directly applicable and enforceable in Spain as a EU member state.

Spain has enacted its internal Law 6/2020, of November 11, on trust electronic services. It complements eIDAS Regulation and repeals Law 59/2003, of December 19, on electronic signature which implemented the former Directive.