U-nets : how exaclty is upsampling performed
The original U-Net paper used nearest neighbor interpolation as far as I know. This is also the default upsampling method in TensorFlow. My own anecdotal advice is to not use transposed convolutions in U-Net. It will only make your CNN slower and won't really increase your F1 score (or whatever metric you're using). I would recommend nearest neighbor interpolation.
Transposed convolution is basically regular convolution with zeros inserted between each input. In U-net after each upsampling, there will be a regular convolution layer. So you don't lose anything if you choose fixed weights like nearest neighbor.
Upsampling outside the neural network domain applies two steps: 1. upsample, 2. lowpass filter. The lowpass filter is here the learnable convolution. In CNN there only seems to be an issue with aliasing (see Making Convolutional Networks Shift-Invariant Again). But this happens also with max pooling / downsampling.