Choosing Between One-Hot Encoding and Label Encoding for Time Series Forecasting

Question

I'm working on a time series forecasting problem with let say 10 categorical attributes, and I'm uncertain about whether to use label encoding or one-hot encoding. Since there's no ordinal relationship among the categories, I'm leaning towards one-hot encoding. However, some variables have over 100 categories, potentially leading to 800-900 dimensions.

Questions:

1. would such high dimensionality be problematic for time series forecasting models like Prophet or neural networks?(I don't think so, but please give your view)
2. Should I consider reducing dimensionality (e.g., PCA or Manifold) after one-hot encoding and obtaining 1000 attributes?

Please provide insights and recommendations based on your experience.