Typically I advise clients against doing an automatic redirect like this. I understand why you feel this is an issue, it’s a not uncommon feeling, however the standard approach works just fine for many sites as large, or larger, than yours and the automatic redirect may not work in some scenarios, leading to poor UX.
The login-once-login-automatically-everywhere you’re expecting is how interconnected services like Meta (e.g. login to Facebook and you’re logged into Instagram) sometimes work because they’re centrally controlled platforms (albeit even centralised services will sometimes work the same way DiscourseConnect does too).
In contrast, you’re dealing with independent open-source software frameworks here (i.e. Wordpress and Discourse). They can be setup to effectively work in the way you’re expecting, but it requires specific custom work that takes into account your specific use case. It’ll never be how an authentication system like DiscourseConnect which serves thousands of different use cases, works.
No, with the caveat that I would question the premise of needing it. But without more information I can’t see an issue with using it.