The great disadvantage of this method of verifying the positions of the site is the personalization of the search. The search results depend on many factors, and for different users it can be completely different.
To see and analyze the keywords for free, you can use the Topvisor Service. Provides free verification of up to 200 words.
Another similar SEO tool is All the positions. Not only can you track positions in search engines, but also analyze competitors and evaluate website traffic by connecting Google Analytics. SE Ranking It is another tool. In the SE classification service for new users, a free trial period of 14 days is offered. By registering on the site, you will get access to a training video, which describes in detail how to work with the service.
These are good services for your demands.