Your intuition is correct.
The "SSR" looks confusing because people are using that in 2 different ways:
(1) Server-Side-Rendering means using Client-Side frameworks like React on the server : https://en.wikipedia.org/wiki/Server-side_scripting#Server-s...
...or...
(2) Server-Side-Rendering means _any_ dynamic page generation on the server side regardless of programming language or framework. That has been done since the beginning of the web with Perl+CGI, PHP, ASP.NET, etc. For this mindset, SSR means "we've gone full circle" because it ignores the Javascript evolution from clients to servers.
The 2 groups are talking past each other. For people using "SSR" definition (1), it's doesn't look "full circle" because a language like PHP was never in a runtime in browsers so there was never a client-side-to-server-side re-use of the rendering code. "SSR" is probably a bad name to describe that trend.