This is common for a huge number of products, ranging from cosmetics, consumables, pharmaceuticals, bottled water, etc.
But if, as you say the largest emission comes from manufacturing the plastic bottle, not the transport of the bottle AND the content; then it seems possible to lower the carbon footprint by switching to glass (on top of the other advantages like reducing landfill use/litterring/environmental pollution).
Lmao, that's on the order of 1-2%.