Why SP groups are not showing while typing in the target audience section of modern communication site OOTB web parts?
Is there any other way to map SP groups in OOTB web part target audience?
SharePoint groups are not supported for audience targeting in SharePoint online modern experience.
Azure AD groups (including security groups and Microsoft 365 groups) are supported with the exception of AAD dynamic groups.
Documentation: Target content to a specific audience on a SharePoint site
Currently you can only use AD groups or Microsoft 365 groups to target audiences.
Source: Audience Targeting for Quick Links Web Part in SharePoint Online
You can vote on below similar SharePoint UserVoice so that Microsoft will implement these features at earliest: