How To Perform a Thorough Website SEO Technical Audit

Google Analytics
Search Console
Screaming Frog
SEMrush
GTmetrix - filter out external resources
Pingdom Tools
LoadImpact
BuiltWith
site:domain.com search in Google
check robots.txt for existence, crawl settings, and XML sitemap location
check favicons
check for most important structured data (Schemas) with Google's Structured Data Testing Tool
check for call tracking
check cost of organic traffic / month
check organic keywords ranked for in Google
check paid search spend
check organic trend in past 2 years
check for Google Analytics / Google Tag Manager
check for martech
check meta descriptions plus review them for uniqueness, length and CTA's
check for CDN
check for mixed content errors
check for redirects
check for canonical tags
check for more than one H1 tag per page
check header hierarchy
check crawl depth
check xml sitemap
check hreflang
check for alt attributes
check for errors
check for links from non-http sites if you have https and try to get them to move to https so you can see referral data (VERIFY)
check for duplicates of anything (h1, h2, title, meta description, etc.)