I too have been thinking a lot about this topic. I have run a couple of training sessions which I think have been useful.
Digital literacy and the School Library is a webinar I recorded last year. I also ran a small group training session around the same topic that you can see here. These currently only can be booked as a group but I am planning to create them as a Moodle course when I get round to it.
I wrote this article that helped me think about this more fully when I was planning the training. You right find it useful.
Getting together with a group of librarians to define the skills would be really useful. Maybe start with the FOSIL skills framework document and go from there… If you need help to use it I am currently creating a Moodle called Raising awareness of your school library and your expertise through your library management system. In one of the sections, I talk through how to use the skills framework. I hope to have this ready by the end of September.
I agree working with teachers within an inquiry project is a great way to encourage use as it also helps teachers understand how the system works.
If you ever get your group of librarians together let me know 😊.