Post content that will be useful in the long run, at least for the next 3-4 years, on your site.
Publish time-sensitive, helpful, or entertaining content that can help people on social media.
Any content that helps you tell your story or show how you have evolved, like a note about business history, an award you won, or coverage you got, can live on your site.
So avoid posting time-sensitive content on your website.
But you can publish evergreen content on social media. For example, convert an evergreen article into a Twitter thread.
For the ideas where you are not sure whether they belong on social or on your own website/blog, post them on social first.
If your audience engages with it and validates the ideas, and matches the long-term relevance criteria, post a more well-rounded version on the website.