Your question is a bit unclear, but if the cruz of it is

If the redesigned site on the new host is found by navigating to the same exact address as the WordPress site, is there a need for redirection?

Then, provided all the pages retain the identical URL's (ie https://...../xxx ) as they had prior to the shift there is no point in doing redirection - and not really any practical way to do so either.

If some of the URL's are different you will want to do 301 redirects from the old URL to the new URL. There are lots of ways to do this - probably the most standard is by editing the .htaccess for the site and adding redirect lines to it like

Redirect 301 /original.html https://canonical.site/new-url.html 

Your question is a bit unclear, but if the crux of it is

If the redesigned site on the new host is found by navigating to the same exact address as the WordPress site, is there a need for redirection?

Then, provided all the pages retain the identical URL's (ie https://...../xxx ) as they had prior to the shift there is no point in doing redirection - and not really any practical way to do so either.

If some of the URL's are different you will want to do 301 redirects from the old URL to the new URL. There are lots of ways to do this - probably the most standard is by editing the .htaccess for the site and adding redirect lines to it like

Redirect 301 /original.html https://canonical.site/new-url.html