You can choose a completely different font set for your website, provided by Google Fonts. Once you do so, the font will be updated throughout the website and will remain consistent whichever block you add.
1. Сlick on the Site style icon on the toolbar in the editor:
2. Navigate to the Texts tab, browse through the font sets library and choose a suitable one:

You can choose a specific font for a particular text type on your site — for example, links, quotes, etc.
1. Access the Texts tab in the Site style, hover over the current site font and click Edit:
4. Publish the site for the changes to appear live.