What’s most important on the list for QA engineer skills? Which skills do you need to see proficiency in and which are you comfortable training?

As @Guilherme has said I would expect all team members to have a solid appreciation of the value and application of testing within their own development practices. Quality of outputs and outcomes is not down to an individual, it is a team sport. I would see the QA Engineer as critical to developing QA knowledge and practices across all team members, and ensuring that QA is as efficient as possible through automation. And also working with everyone including stakeholders to ensure that work specifications are testable up front,  and that code produced is demonstrably working correctly.

I would prioritise the following capabilities

Communications skills
Scripting and automation skills
Ability to coach others on testing practices and requirements specification
Ability to discuss and evolve work to meet desired outcome specifications so they can be reliably and demonstrably tested during the development lifecycle

The role of the QA engineer in my view is to lift the testing competency and practices across the entire development team, and ensure testing is as efficient and effective as necessary for the business/regulatory context of the individual application/organisation.

In my view, it is more crucial to determine whether QA skills will be designated, as a specific "role within the team" or as a competency expected of every Software Developer, rather than just focusing on having well-defined QA skills.

Obviously, this is a complex discussion, as each type of software has different needs, but in many scenarios, I am certain that a QA engineer is not necessary, and the QA functions should be within the responsibilities of the Software Developer.

I recommend the book "Software Craftsman, The: Professionalism, Pragmatism, Pride" for further reflection.

As Vatsan said, scripting and test automation are key skills. A strong understanding of the business use cases is also invaluable. I would want to see proficiency in their analytical abilities, and train for the rest.

In addition to below, the QA Eng would also need some below.
    Understand the business use cases and users.
    Understand scripting and test automation.
    Understand the impact of each test.

Ciao, I believe it depends of the project and business sector anyway I am for a bunch of:
- Analytic thinking;
- Communication skills (for reporting especially);
- Attention for the details.