I'm aware that there are criticisms of blindly applying checklist approaches, with associated summary scores, in quality appraisal, but what are the alternatives and where can I find the literature that discusses these? Thanks
I agree with Helena Rezende, the Joanna Briggs Institute is a top reference on this topic. I also recommend to have a look on the equator network, because quite every big journal recommend to choose a method within this site. https://www.equator-network.org/?post_type=eq_guidelines&eq_guidelines_study_design=qualitative-research&eq_guidelines_clinical_specialty=0&eq_guidelines_report_section=0&s=
You can use, for example the Standards for reporting qualitative research (SRQR).
GRADE is one of the best for quantitative systematic review: https://bestpractice.bmj.com/info/toolkit/learn-ebm/what-is-grade/#:~:text=GRADE%20(Grading%20of%20Recommendations%2C%20Assessment,for%20making%20clinical%20practice%20recommendations.
There is actually a systematic review discussing the different type of quality/bias tools: Article The methodological quality assessment tools for preclinical ...
This literature gives you everything including the Joanna Briggs institute scale, The New castle of Ottawa for observational studies and the Cochrane risk of bias tools for systematic review