Make a page available on a private SharePoint

Steps below:

1. Go into the Site Pages Library
2. For the Page you want to make public, click on the three dots ... then Managed Access
3. In the Popup, click on the three dots ... then click on Advanced Permissions
4. On the top-left, click on Stop Inheriting Permissions and click on Ok in the popup
5. On the top-left, click on Grant Permissions and add Everyone except external users (includes everyone in your company) and give it Read access

This will give everyone in your company Read access to just that page.

Note that when they go to this page, they will also see the site menu which might contain links to items in the site they don't have access to (depending on how you've added the links) - and when they click on them, they'd get an access denied error.

I'll recommend rethinking if this is the right approach though. It might be better to create a new site open to everyone and keep the locked down site still locked down as it is - this is the safer option.