I found a possible answer in
the same largest online astronomy textbook.
Quote:
Luminosity
The stars of the Eta Carinae system are completely obscured by dust and opaque stellar winds, with much of the ultraviolet and visual radiation shifted to infrared. The total electromagnetic radiation across all wavelengths for both stars combined is several million solar luminosities (L☉).[19] The best estimate for the luminosity of the primary is 5 million L☉ making it one of the most luminous stars in the galaxy. The luminosity of Eta Carinae B is particularly uncertain, probably several hundred thousand L☉ and almost certainly no more than 1 million L☉.
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The bold text above might explain the reddish hue ?