Open Source SEO Software
SEO software is mostly a crawler plus a database of what your site does in search, wrapped in a subscription that you feed your own site and keyword data into. The established suites are expensive precisely because that data exhaust is valuable to them, not just to you. The open source options here run the auditing and rank tracking on your own machine, keeping the crawl results and your keyword strategy in-house.

OpenSEO
Open source SEO platform for keyword research, backlinks, rank tracking, site audits, and AI visibility

SerpBear
Open source search engine position tracking and keyword research app with email alerts and a built-in API

SiteOne Crawler
Cross-platform website crawler and analyzer for SEO, security, accessibility, and performance

SEOnaut
Open source SEO auditing and reporting tool for site scans, issue severity, and technical SEO checks
LibreCrawl
Web-based SEO crawler for website auditing, link analysis, and export without subscription fees

Site Audit SEO
Web service and CLI for SEO site audits with crawl, Lighthouse checks, and browser reports

RustySEO
Cross-platform desktop SEO and GEO toolkit to crawl websites, analyze server logs, and optimize pages

SEO Panel
Open source SEO control panel for managing multiple websites, with rank tracking, auditing, and backlink checks