I would not think interpolation would be that much easier than a creating a TIN. I have not looked at the dataset though, so it might be "pre-interpolated" (probably using a TIN if I had to guess), in which case this would be pretty easy with something like pyqgis on a flask server or whatever. The entire api could basically just be:

    @app.route("/elevation")
    def elevation():
      fileName = "/path/to/raster/srtmRaster.tif"
      fileInfo = QFileInfo(fileName)
      baseName = fileInfo.baseName()
      srtmRaster = QgsRasterLayer(fileName, baseName)
      res, ident = srtmRaster.identify(QgsPoint(request.form['lat'], request.form['lon']))
      return ident[0]

I can test this out and throw it on github with some polish if anyone is interested.