There are several reasons why positions differ from the project report and from independent search verification.
Updating search results
Search engine databases contain a huge amount of data and are simply not able to be updated at the same time. While the system recalculates the indexes of all existing pages, jumps in positions may occur at this moment.
In addition, Yandex uses a distributed network of servers to optimize its work. When you enter a request in the search bar, it is sent to one of the front servers for processing. Different front servers may return different results until complete synchronization.
Search personalization
To ensure that sites on the first page of results match the user's query as closely as possible, search engines individually adjust search results based on preferences and statistics of previous queries.
If you want to see the actual positions of a site, you will have to disable personalized search. To do this, on the Yandex main page, go to the "Settings" section - "Portal settings" and uncheck all the boxes related to personalized search.
You can also check the actual positions from the "Incognito" mode or after clearing the browser from cache and cookies.
Regionality
When checking the positions of your site for key queries, make sure that the settings indicate the region for which the resource is currently being promoted.