Minecraft -- Advancement criteria that targets specific villager professions

I am trying to create an advancement criteria for 1.16+ where the advancement is granted after a player interacts with a specific villager. So far I have this:

"criteria": {

"test1": {

"trigger": "minecraft:player_interacted_with_entity",

"conditions": {

"entity": {

"type": "minecraft:villager",

"nbt": "{VillagerData:{profession:"minecraft:fletcher"}}"

} 
} 
} 
}

However this doesn’t seem to work. I have played around with brackets and quotations but no change. Am I going about this the wrong way? Help would be appreciated.