chore: update fallback Coder icon to reflect new branding [DO NOT MERGE] #18517
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Caution
This PR should not be merged in until Tuesday on June 24, right before the code freeze
Addresses part of the frontend changes needed for #18516
Changes made
[x] Updated the Coder logo to use the one from the new brand
[x] Updated icons/coder.svg to use new logo
[ ] Remodeled and updated favicons
Dark:

Light:

Dark Emoji Picker:


Light Emoji Picker:

