Here are three methods to solve this issue.
1.Go to Site contents -> Site pages -> Library settings -> Versioning settings -> Content Approval -> Set Require content approval for submitted items as No.
After setting, posts without approval can be seen in the News web part and Site pages library.
2.Go to Site contents -> Site pages -> Library settings -> Versioning settings -> Draft Item Security -> Set Any user who can read items.
After setting, users with default read permission can see posts without approval in the Site pages library.
But in the News web part, posts need to be published and approved, then can be seen.
3.Create a permission level named Read with approval.
(1)Go to Site permissions -> Advanced permission settings -> Permission Levels -> Read -> Copy Permission Level -> Select Approve Items - Approve a minor version of a list item or document -> Create.
(2)Go to Site contents -> Site pages -> Library settings -> Permissions for this document library -> Grant users with Read with approval permission.
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