Exactly as stated is the Solar Manifestation magic and can it be detected by detect magic?
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Yes
Detect Magic detects "all magic spells, effects, items, and objects (including those on or affecting creatures you can see)" (Starfinder Core Rulebook pg. 348). Solar Manifestation is a supernatural ability as denoted by the "(SU)" tag (SCR 101). Supernatural abilities are explicitly magical (SCR 59).