I run it in roughly this order, because each step tells you where to look in the next:
1. Crawl the site with Screaming Frog (free up to 500 URLs) or similar. Look for 4xx/5xx, redirect chains, missing or duplicate titles, and pages carrying a noindex you didn't mean.
2. Search Console, Pages report. Compare what Google has indexed against what you think should be indexed. The gap is usually where the real problems are.
3. robots.txt and the XML sitemap. The sitemap should only list URLs that return 200, are indexable and are the canonical version.
4. Canonicals and duplicates: parameter URLs, http vs https, www vs non-www, trailing slashes.
5. Core Web Vitals report in Search Console, then PageSpeed Insights on the worst templates, not every single page.
6. Internal linking: important pages sitting 4+ clicks deep, or with no internal links at all.
The trap is ending up with a 200-line list nobody acts on. Group the issues by template, since one fix to a template usually clears hundreds of URLs at once.
