@blind-confused, can you please confirm whether or not you can re-add your search engines using OpenSearch indexing as I explained in my previous reply?
Additionally:
This functionality has never been available in the address bar unless you’re using search shortcuts, which can be edited on the brave://settings/searchEngines page. What you seem to be referring to is the search widget on the New Tab Page, which allows you to click the icon and select what engine you’d like to use from the list of default search engines:
The reason you are likely only seeing Startpage is because you have not added any of the search engines to the default list yet. Please see the reply I left above with video instructions on how you can add more engines to the default list.