Sure, no problem!
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Replace the logo with an embed element
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Place this piece of code inside it:
<svg xmlns="http://www.w3.org/2000/svg" id="Layer_2" viewBox="0 0 1000 1000"><defs><style>.cls-1{fill:currentColor}</style></defs><g id="Layer_1-2"><path d="M709.48 376.7c28.69-28.69 26.58-58.61.53-84.65-25.88-25.88-54.75-26.59-83.26 1.93l-16.03 16.01 82.73 82.73 16.03-16.01ZM693.79 607.6l-82.73 82.73 16.01 16.03c28.52 28.5 57.39 27.8 83.25 1.93 26.06-26.05 28.18-55.96-.53-84.65l-16.01-16.03Z" class="cls-1"/><path d="M500 0C223.86 0 0 223.86 0 500s223.86 500 500 500 500-223.86 500-500S776.14 0 500 0ZM359.67 772.37 236.46 649.15l88.01-88.01 19.88 19.9-64.24 64.24 29.75 29.75 59.5-59.49 19.71 19.71-59.49 59.49 33.97 33.97 65.47-65.47 19.9 19.88-89.25 89.25Zm69.35-435.61-65.47-65.47-33.97 33.97 59.49 59.49-19.71 19.71-59.5-59.49-29.75 29.75 64.24 64.24-19.88 19.9-88.01-88.01 123.21-123.21 89.25 89.24-19.9 19.88Zm73.74 197.81c-19.09 0-34.56-15.47-34.56-34.56s15.47-34.56 34.56-34.56 34.56 15.47 34.56 34.56-15.47 34.56-34.56 34.56ZM609.14 271.1c39.42-39.42 84.65-45.23 125.85-4.05 39.59 39.61 36.42 88.19-2.83 127.44l-42.59 42.59-123.21-123.21 42.78-42.78Zm126.19 462.18c-41.19 41.19-86.42 35.38-125.86-4.04l-42.76-42.78 123.21-123.21 42.59 42.59c39.25 39.25 42.42 87.84 2.83 127.43Z" class="cls-1"/></g></svg>
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Set the font color of the embed to “#0a0a0a”. This will make it the color it should be.
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Animate the text color of the logo to the color white.
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Do the same as step for but in reverse for the second click.
And voilà. You now have a color switching logo!