Eleda asked a common question the other day that could save a lot of Shopify store owners a lot of problems around new themes:
Do apps, like your JSON SEO app (and my pile of other apps) have to have anything done in order for them to function when a theme is updated?
The general blanket statement is that you'll need to check each app to see if its code is installed and working correctly. If not, you'll need to reinstall its code and follow any setup process they have.
You don't need to uninstall and reinstall the app as a whole, just the code.
You also only need to do this on apps that touch the storefront. e.g. My Repeat Customer Insights app is purely on the Shopify backend so it doesn't care about theme changes at all.
(Shopify's version of the blanket statement is to uninstall and reinstall every app which is super excessive and can cause problems)
That's just a blanket statement though.
On one side are apps that might need the full app uninstalled and reinstalled. On the other side, some might automatically update your theme for you when you publish the theme.
In JSON-LD for SEO's case, Shopify will tell the app when you've published a new theme and the app will automagically update the code it needs. There's also a button in JSON-LD for SEO to reinstall the snippet to the current theme, it's the same thing it does automatically but it lets you push a button to reinstall/refresh the code (e.g. in case it was removed on accident).
Upgrading a theme or switching to a different theme can be a big deal in Shopify. The process of switching is easy (click a button) but the impacts can be far reaching (I'm not even touching on the SEO or conversion impacts which can fill a book...)
Test the new theme, be careful, and make sure you have a backup plan in case things go sideways.