I want to color the background of svg text similar to background-color in css
I was only able to find documentation on fill, which colors the text itself
Is it even possible?
No this is not possible, SVG elements do not have background-... presentation attributes. 
To simulate this effect you could draw a rectangle behind the text attribute with fill="green" or something similar (filters). Using JavaScript you could do the following: 
var ctx = document.getElementById("the-svg"),
textElm = ctx.getElementById("the-text"),
SVGRect = textElm.getBBox();
var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
    rect.setAttribute("x", SVGRect.x);
    rect.setAttribute("y", SVGRect.y);
    rect.setAttribute("width", SVGRect.width);
    rect.setAttribute("height", SVGRect.height);
    rect.setAttribute("fill", "yellow");
    ctx.insertBefore(rect, textElm);
You could use a filter to generate the background.
<svg width="100%" height="100%">
  <defs>
    <filter x="0" y="0" width="1" height="1" id="solid">
      <feFlood flood-color="yellow" result="bg" />
      <feMerge>
        <feMergeNode in="bg"/>
        <feMergeNode in="SourceGraphic"/>
      </feMerge>
    </filter>
  </defs>
  <text filter="url(#solid)" x="20" y="50" font-size="50">solid background</text>
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