I am not sure about your use case. There exist many JS libraries which will generate client side QR codes. How many of them do you handle that you optimize for file size? Or is it just an academic interest?

SVGs are XML so technically, yes, you can just embed your visually encoded payload data with namespaces attributes and elements. If you don't want to use namespaces, you can use off-canvas texts, hidden/opacity=0 texts or even XML comments. You can even use the regular metadata section of SVGs. You can make the whole QR code within the SVG a clickable link.