Looking to implement redirects for entire website and a specific page

I am looking to implement the following.
if someone visits the site
oldsite.com or any of the pages under it they will be redirected to newsite.com

BUT
i need a specific page on oldsite.com to redirect to something else.

oldsite.com/page should go to newsite2.com

To summarize.
oldsite.com and any pages under that -> newsite.com
oldsite.com/page -> newsite2.com

I have tried using the Cpanel redirects but it doesnt seem to work for the specific page.

Adding

RewriteEngine On 
RewriteRule ^(.*)$ http://www.newdomain.com [R=301,L]

to htaccess file as well. I cannot seem to figure out how to do the last part of redirecting the specific url to another website while keeping the redirects to everything else.

Redirect your specific page first, then any 'remaining' URLs second:

RewriteEngine On
RewriteRule ^myspecialpage$ http://www.specialdomain.com/myspecialpage [R=301,L]
RewriteRule ^(.*)$ http://www.newdomain.com/$1 [R=301,L]

If you want to redirect everything else to the homepage (not the same URL at the target domain), then you can use:

RewriteEngine On
RewriteRule ^myspecialpage$ http://www.specialdomain.com/myspecialpage [R=301,L]
RewriteRule ^(.*)$ http://www.newdomain.com/ [R=301,L]

You can use the more "simple" mod_alias directives:

# Redirect specific page
RedirectMatch 301 ^/page$ https://newsite2.example/

# Redirect everything else
RedirectMatch 301 ^/ https://newsite1.example/

Note the order of the directives. The most specific redirect is first.

This assumes the old-domain is not pointing to the same place as newsite2.example and/or newsite2.example.

You should test first with 302 (temporary) redirects to avoid potential caching issues.

NB: Never mix redirects from both mod_alias (Redirect and RedirectMatch) and mod_rewrite (RewriteRule) since you can get unexpected conflicts. (mod_rewrite is always processed before mod_alias despite the apparent order of the directives in the config file.)

And, as mentioned in comments, if SEO is a concern then many-to-one redirects to the homepage like this are likely to be seen as soft-404s by search engines (and generally gives a bad experience for users).