GOOGLE SEARCH ENGINE CRAWLING AND INDEXING query --

Hello all, I have recently taken a website live and the organic footfall is less. Now when I search myDummyWebsite.uk in google search I get back the proper desired search result UI - a) having the proper meta title tag on top, b) backlinks to my same domain as the subheadings for my website, c) proper meta description tag which is ideal. But when I search just myDummyWebsite the search result shows my correct page myDummyWebsite.uk as the top search but now does not take into consideration the meta tags whatsoever - and in turn shows the first content block wrapped around H1 and H2 as the meta description of the search result for the same website. I am a developer and fairly new to SEO and have explored the Google Search Console (GSC) much which might help in this regard but to little use as it needs the domain cred but my contractor who has the creds to the website domain is hardly available to get into the GSC.

Query :: Why does google search result show a different meta title and description of the same site for two different key searches - but these keys differ by only the top level domain present in the search. How do the crawlers and indexing work here and why is it so different.

I have tried changing the meta tags and it does the job for abc.com the search with Top level domain gets updated but the abc search result still has the newer H1 and H2 wrapped content as the meta description of the google search result.