You need to explicitly invite external users via their email address. SharePoint Online doesn't provide an 'anonymous' option for site-wide access (it will at the file-level).
Sharepoint site share with everyone option missing.

I created a site with SharePoint that I want to external users to join; However, when I type everyone in the name in only option that appears is "Everyone except external users" I want to include external users how can I do that?
Microsoft 365 and Office SharePoint For business Windows
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Jerry Xu-MSFT 7,961 Reputation points
2020-10-23T02:33:59.003+00:00 Hi, Omar-6618 ,
If you want to show everyone option in people picker, you can try with the following cmdlet in PowerShell. When users share an item with Everyone, it is accessible to all authenticated users in the tenant's Azure Active Directory, including any active external users who have previously accepted invitations.
connect-sposervice -url https://domainName-admin.sharepoint.com -cred(get-credential) Set-SPOTenant -ShowEveryoneClaim $True
In other words, this everyone group only contains the external users who has accepted the invitation to your tenant, and recognized as an external user in you Azure AD. It will not work for external users who are not invited. Just like Trevor said,
SharePoint Online doesn't provide an 'anonymous' option for site-wide access (it will at the file-level).
SharePoint Online has deprecated the public site feature years ago and will not support making a site accessible by anonymous users from Internet.
Reference: https://learn.microsoft.com/en-us/sharepoint/troubleshoot/sites/public-websites-be-discontinued
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