Embed single group/member tile in a post?

Hello @mungbean
You can use Shortcode for BuddyPress plugin to embed a specific Groups/Member on a specific post or page by using given parameters.
Plugin URL: https://wbcomdesigns.com/downloads/shortcodes-for-buddypress/
KnowledgeBase URL: https://wbcomdesigns.com/kb-category/shortcodes-for-buddypress/

Example :
Used shortcode : [groups-listing search_terms= “Kill Bill”]
Output: https://prnt.sc/w6xju5

Hope the above helps!
Let me know if you have any further queries.

Thanks, I will take a look at your suggestion