@levanii It’s normal to not get the same score every time you run a PageSpeed Insights test, with many factors taken into account during testing.
Site Kit itself is mainly a backend operated plugin. After setting up the plugin the only addition added to the front end is the below meta generator tag, which you can see when inspecting your sites source code with just the Search Console module connected:
<meta name="generator" content="Site Kit by Google 1.10.0" />
This meta tag has minimal performance impact, just one line of code and no additional requests.
If you choose to connect the Analytics, AdSense, Tag Manager or Optimize modules the snippets are added to your site, although no different to manually placing the product snippets yourself, outside of Site Kit, with little performance impact.
When connecting the other Google services via Site Kit (or manually) there may be other considerations which may have a minor impact on performance. An example would be the content you choose to place inside your Tag Manager containers, such as third party scripts or product snippets. In many cases such features make third party requests which contribute to your sites performance. I would suggest in your case to perform the same test with only the Search Console module active.
Finally if you’re using the latest version of the PageSpeed Insights module within Site Kit we’ve made changes to better reflect the user experience on your site. If you’ve updated to version 1.10.0 you’ll notice the changes, and we’ve added a blog post on this to the plugin website.