Your question is “Should I create separate social media account for every website?”
Near to me It is better to create a new social media account or ID for each website.
Why Separate ID?
When you target a specific niche then your audience like your account due to their interest in the content. If you will create only one account on Twitter, Facebook page then you will grow your likes and followers but engagement will not as you want.
For example, if you have a quote website and people like your Facebook page. and on the other hand, you have medical books related website and one of them like your same page also. So a user who liked your Facebook page just because of the quote his interest regarding medical post will be zero. If you post more content regarding medical then that user will avoid your facebook page.
But if you have the same page with the same website then your followers will love to read your social media post and your engagement will be good as compared to the above-mentioned situation.
So you should always create a new id or page for each website.
However, If you have almost the same niche such as SEO, Blogging, Technology then you can use the same account. But if you have different niche e.g quotes, medical and songs related then you must use a separate account.