A question about homemade chili garlic paste - how long will it last in refrigerator?

I agree with all of the above, add an acid (e.g., vinegar) and this will last for ages in the fridge. In fact, in the height of hot pepper season, I pulse peppers, sugar, vinegar, ginger and salt and keep it in a jar throughout the winter and it is so fab and versatile! Mix this with a thick simple syrup and you've got a fantastic sweet and spicy pepper sauce. If you want to take this a step further, you can leave it at room temp to ferment and get truly amazing and health promoting properties and intricate flavors (as well as a product that will last...not forever..but...). If you want to try such a thing, I suggest searching the internet for fermented pepper pastes, you need to get the salt/acid ratios in proper order.

Dehydration works by denying bacteria water which they need to replicate. Rehydrate and things can grow.

Garlic, like anything that comes from the ground, can harbor botulism spores which replicate in anaerobic (oxygen poor) environments even under refrigeration (which is why homemade garlic oil = bad news). Judging just by the listed ingredients, that would be the reason for a short useful life.

Commercial flavored oils and salad dressings are properly acidified to prevent botulism.

Without the recipe, I'm going to assume that it's because the paste is not cooked. My aunt's recipe for chili garlic paste/sauce involves no oil, plenty of sugar and cooking. It keeps in the fridge for a couple of months and frozen for up to a year.