In case anyone else runs into this issue (of your website not being crawlable by Google) - this is how we solved the issue:
We created the robots.txt template in our theme.
We added the following code:
User-agent: Googlebot
Disallow:
User-agent: Googlebot-image
Disallow:
in line with Google’s documentation here and here.
This resolved our Merchant Center issues, and also resolved our Search Console issues (our domain was not being crawled by Google - in Google Search Console we had the warning “Indexed, though blocked by robots.txt”).