I have been listening to your recording actually for a beginner this is verry good.
Try to play every note at the same tempo and the same lengt so you are able to feel what is going on each time you play the note this will give you more accuracy and yes slow at the start no need to rush.
Playing the 2 draw is first hitting the 2 draw accurate second relax when inhaling explore with it until you get it right and when you do try to remember what it feels like and repeat this over and over so it becomes natural.
My first times playing the harmonica i was thinking the harp was broken because the 2draw was squeeling when i played it, it took me a while to discover that it was me playing it the wrong way ☺️✌️
Hope this will help.