I have looked at my Google Maps Profile and I have also tried looking under my Contributions.
When looking at one of my reviews, selecting my photo and level, it opens the Local Guide window that shows how many contributions I have made. There is nothing to indicate my number of Badges or which Badges I have earned.
I have read through the Local Guides Connect FAQ, Help, and the Google Maps Help page.
Where is it that I should look as I feel I have exhausted my possibility on a location.
I believe you are following a sequence of actions as below.
Open any one of the visited POI and access the reviews section. There you find the one posted by you at the top. Next, a click to the profile icon takes you to the contributions page. Here you are getting perplexed by not seeing the badges as was visible in the old user interface.
However, here you will find small and grey coloured inequality sign “>” next to the count of points. A click on that and that will lead you to the next page displaying all the badges.
As @ErmesT stated in his response, the badges can be seen on your Google Maps application on your mobile device, and at the moment they are not available on the desktop version. I am going to accept his answer as a solution to your query, but please feel free to check @MortenCopenhagen and @C_T 's responses as well, because they provide very useful input.
Yes @musan , the badges are visible on the App only, as stated in my previous reply.
Most probably during the transition to the new Connect the "solution disappeared, fo I am flagging it again to makes more clear for the readers where to find their badges