How to change the wording of front-end `next article` for custom type registered in a plug-in?

Most likely this is coming from the Theme’s language file, can you explain why the translating has to be done by the plugin? Language files are designed for this.

But, if you really want to do this, use the gettext filter:

https://codex.wordpress.org/Plugin_API/Filter_Reference/gettext

Using this to much may impact preformance.
https://pippinsplugins.com/dangers-gettext-filter/

Regards, Bjorn