If you notice your site is taking a long time to load, then you should first use PageSpeed Insights to see what can quickly be optimized (also check your file sizes, hosting server, NGINX and other common sources of slow speed, too.) And, if you've notice gradually fewer Organic Search visits, PageSpeed Insights might be able to help. As Google is reducing the prevalence of slow sites, you could be losing traffic. Speed up your page load times by finding what is blocking renders, slowing down contentful paints, and other critical page speed signals.
If you have any problems with your rankings or a decrease in ranking position within google it is very good to make an Link Audit with the Link Research Tools. Then you Screen all Links manually and setup your disavow-file easily. With the Link Detox Boost you gain Rankings back so fast. The last time we used it for a client, we got back the rankings within a week to 170 Positions within the Top Ten, even Position 1.
calculates the opportunity or risk of potential links that are not built yet, so you can go only after the good ones
gives you fresh data from 26 link sources and lets you analyze the full backlink profile. Google search console gives you only a sample of your backlink profile.
powerful link prospecting made easy
possibility to connect with Pitchbox (professional outreach tool for link removal and link building campaigns), SEMRUSH, Ahrefs, GSC
I think GTmetrix has some feedback that PageSpeed doesn't provide, but Google's tool is easier overall and has a better user experience; also offers compressed images, CSS, and javascript files if that's the case. Also, Google has extensive documentation to help you better understand what can be done to improve your grade.
LinkResearchTools is much more advanced in analyzing links. Period. All the other mentioned tools have many useful features for SEO but LRT is definitely the way to go for backlink analysis, link building, and competition analysis. They also offer very nice and quality courses for improving SEO knowledge. I already attended one of them and I am very satisfied with the knowledge I gained.