To fix incorrectly indexed Google Pages through the Search Console – URL Inspection Tool

My website is indexed incorrectly and displays a different header than the one that was updated on my website.

If I used the URL Verification Tool in Google Search Console, the index displays the following incorrect information:

URL check Wrong information in the Google index

When I search for "Live Version" with "URL Inspect", the correct information is returned, as shown below:

URL Inspect - correct information about the live test

In my understanding, the results should be the same, assuming a delay in indexing, but the results will remain different for a long time. When I search Google for my indexed page, incorrect information is displayed (see below):

Displayed SERP Inccorect information on Google

How can I fix this and display the correct information on the indexed page?