She doesn't seem happy.

Literal

She [topic-は] not-happy [seems-ようだ].

~ようだ ('seems, appears') is one of Japanese's evidential markers, specifically used when the speaker bases the judgment on direct or inferential evidence rather than hearsay. Attaching it to a negative i-adjective is direct: 嬉しくない ('not happy') + ようだ ('seems') = 'seems not happy.' The construction reads as a careful inference — the speaker isn't claiming privileged access to her feelings, just reporting how things look. In casual conversation みたい would typically replace ようだ; in writing or polite speech, ようだ holds.