Regarding sitelink searchbox

Hi. I’m in the process of switching my food blog theme, actually starting all over again!. I did a quick comparison of my new theme (where I’ve RankMath installed), with the old one (with Yoast SEO installed).

It looks like the old theme has this extra item ‘Sitelink Searchbox’ detail on the Rich Test Results of Google, and I can see my website details in there. But this ‘Sitelink Searchbox’ detail is totally absent on my new theme. Is this normal?

For context, I’ve enabled the ‘discourage search engines from indexing this website’ in settings of my WordPress.

For reference, I’ve tested this link for rich snippets:

Old theme that shows sitelink details – https://www.veganbell.com/vegan-chickpea-scramble/

New theme that does not show sitelink details – https://wordpress-330271-1385410.cloudwaysapps.com/basil-pesto/