I absolutely would not use it in my veggie garden. The materials used to make them often contain adhesives, resins, and chemicals that can release harmful substances when burned. The resulting ash may contain toxins that can negatively impact your soil and plants.
Natural wood ash is the only wood ash I will use. It normally tests out @ potassium (K) ~5%, calcium (Ca) ~25%, phosphorous (P) ~2%, and magnesium (Mg) ~1%
Of course, unless you have a soil test, it is very easy to apply wood ash in excess creating soil imbalances that can lead to significant problems. For example, potassium toxicity can interfere with the uptake of other crucial nutrients, particularly calcium and magnesium, leading to plant deficiencies.
Likewise, excess phosphorus can disrupt the photosynthetic process in plants, hindering their ability to convert sunlight into usable energy. This can result in diminished growth, chlorosis, and overall reduced vigor in garden plants.
Soil imbalances are often very difficult and time consuming to overcome.