When adding a site to Google Search Console you’ll probably need to add it four times. One for WWW, one for without, one for secure WWW and one for secure without. From bullet point #4 from here:
If your site supports multiple protocols (http:// and https://), you must add each as a separate site. Similarly, if you support multiple domains (for example example.com, m.example.com, and www.example.com) you must add each one as a separate site.
All sites going forward (or for the past year or two) should be HTTPS however they’ll probably technically support HTTP. Also, there’s a very good chance most of your external links will point to the non-secure version (including non-electronic links such as radio, TV, business cards, posters, t-shirts, urinal cakes, etc.) so you’ll want to claim those from Google anyway.