Loads should be accepted as synonym for lots.
"I have missed you much/a lot" is the literal translation to this. If you wanted the translation to be "I have missed you so much" shouldn't the danish phrase be "Jeg har savnet dig så meget"?
looking at the sentence construction in the earlier parts of this chapter - the adverb was between har and the pre perf - could this sentence also be written as ' Jeg har meget savnet dig' as well?
"Jeg har savnet dig meget!" - The Duolingo owl email five minutes after being gone.