How to override Breadcrumb theme template?
As mentioned by @Clive, breadcrumbs are not entities so I was not be able to get it done by adding a mytheme_theme_suggestions_breadcrumb_alter. Instead to solve the problem I had to do the following. On top of this, I ended up downloading and enabling Easy Breadcrumb to further modify the Breadcrumb


Copy the breadcrumb.html.twig file from the Classy theme into my mytheme directory
Clear cache
make any edits into the sites/themes/custom/mytheme/templates/navigation/breadcrumb.html.twig file
save and clear cache (if necessary)