This is similar to how I used to do it when I was still an academic, 20 years ago. My mental process is answering questions: is this an interesting paper with something to tell? Do the authors know their field (references)? Are they able to write a coherent and well structured article? If that all checks out, you start reading the paper in more depth.
The 2024 version of this would of course be "hey chat gpt, summarize this article for me and list the key points and then criticize the work". I expect, article quality should improve a lot simply because authors are also using LLMs to help them polish their articles. There's no excuse for submitting unpolished work at this point.
A lot of what I did as an academic was reviewing papers for workshops, conferences and journals. That's a chore that is part of academic life and getting good at that is a core skill.
It's the really bad papers that are the most work. Because after you have a suspicion that something is garbage (this is the easy part) you actually have to read the damn thing in order to deconstruct it properly and provide detailed feedback to the authors that is both fair and actionable. A well written paper is much easier to review and more fun to read. Unfortunately, well written papers are quite rare. Mostly you are dealing with awkward grammar and style (inexperienced researchers, non native speakers, etc.), people who are unaware of key references they should have cited, a lot of bullshit conclusions and shoddy methodology, poorly structured arguments, etc.
You can learn a lot about writing by reading a lot of bad writing and having others criticize your work. I'm really grateful for all the people who took the time to deal with my early efforts. It wasn't great, I know that. I'm not a native speaker. I had to learn writing on the job.