Reality check: ALL writers seeking publication, traditionally or self-published, need a website.
A website will be the first port of call for any potential reader. They will go to your website to get the latest information about your various projects, both old and new. Yes, your social media will likely have information about the latest happenings. However, any older material will quickly be buried. Everything else that you do should point back to your website and the one, central hub where readers can get the most up-to-date information about your work.