Do I need do something else or just wait for a while (if so, how long?) for it to become available for download?

No, normally it should be directly accessible.
However, I see why it doesn’t work: your model repository only contains modeling files (config.json and pytorch_model.bin), but no tokenizer files (such as vocab.txt). Hence, only loading the model will work. You can easily save the files of a tokenizer as follows:
tokenizer.save_pretrained("path_to_directory")
You can then upload those files to your repo on the hub.