Is 你今天早上怎麼樣? or 你這個早上怎麼樣? okay for asking "How are you this morning?" and
没有这个问法，一般工作环境会问“早上好”，不会问“你早上怎么样？”

Chinese people do not say it like this; they always say 早上好 (zǎoshang hǎo) = "morning" or 你早上怎么样？(Nǐ zǎoshang zěnme yàng?) = "good morning".