WP Rocket should be fine. It’s possible you’ll need to make some adjustments to break the cache on WordPress pages that are displaying Discourse comments. There’s a good suggestion here: WP Discourse comment webhook does not trigger a WP Rocket Cache refresh - #13 by Brandon007. The WP Discourse “ajax load” option is also a reasonable workaround.
This seems like the real problem:
[2024-03-14 06:02:59] comment.ERROR: sync_comments.response_error {"message":"Forbidden","discourse_topic_id":"","wp_post_id":13514,"http_code":403}
That’s saying that Discourse is returning a 403 response (forbidden) when the WP Discourse plugin attempts to pull in comments. (The error is being logged from here: wp-discourse/lib/discourse-comment.php at main · discourse/wp-discourse · GitHub)
It’s a bit of a guess, but this plugin suggests that your WordPress site is behind a proxy:
It’s possible that’s triggering the 403 error on Discourse. Maybe the request headers aren’t configured correctly? It’s not something I know a lot about. But, you might be able to confirm if it’s an issue by publishing a post from WordPress with your Discourse site’s Error Logs page open.
Click this link to get to the error logs page:
I think a 403 response will trigger an entry in the logs. If it does, share the (redacted) error message here.