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Outlook cannot read fallbacks if they are non-Office standard fonts; in this case, you'd need to define .primary-font with 'Noto Serif', serif; in your first CSS block, then define .primary-font with Arial, sans-serif !important; afterwards. Remember your cascading rules. Additionally, you should probably define your non-MSO font-family to have a fallback after Noto Serif due to patchy webfont support on platforms such as Gmail—you can just define with serif, but that's a bit less than ideal.
Custom fonts and Outlook (non-browser based) depends on if the custom font is installed on your computer. If the font isn't installed on your computer, no matter how you change your CSS, you won't see it.