No, the rarity of the drop is not influenced by anything it's all just luck.
The level of your invested skill in provisioning and base character level may change the level of the recipes found however.
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Provision writs always reward a recipe. About 10% of the time it’s purple. The recipes rewarded are entirely based on your provision rank. If you are looking for lower level purple recipes, a good way to find them is to set an alt to the appropriate provision rank and have them do daily writs to eventually earn the recipes.
If you’re looking for c150 top level recipes, the drop rate on these right now is about 1:1200. You can do writs daily on six characters and see one in six months. Therefore, the fastest way to earn top level recipes is honestly to farm anything else (motifs or raw mats tomrefine for gold tempers are good options), then sell these and buy the recipes for ~75k. You can easily make a million gold in the time you will spend trying to grind the stupid c150 recipes.
Best way to get top tier purple recipes are guild stores. I sell mine for 5k and they sit in the store for weeks.
Atm I have my main doing max level provision writs and 4 alts doing lower level provision writs so I can get the purple recipes, which I will then use on my main.
There is a master recipe list online and purple recipes only come from level 2 provision writs onward.
level 2 and 3 only have 1 drink, 1 food purple recipe.
for some strange reason lower level recipes sell for a lot more gold than max level ones do.