Hi @Rishikesh Rai
Currently there is no such rest api to get all items which current user have specific permission. You can use following api to get permission of one of the folder and check if the user have edit permission to the folder.
/_api/web/GetFolderByServerRelativeUrl('DocumentTest/testfolder')/ListItemAllFields/roleassignments?$expand=Member,RoleDefinitionBindings
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