One option is to make a free account with datapane (https://datapane.com/) and use the geemap package (https://geemap.org/) which has functions for turning a GEE layer into an interactive datapane object, which can then be imbedded in html.

See here for a tutorial on using geemap to make an interactive datapane object: https://colab.research.google.com/github/giswqs/geemap/blob/master/examples/notebooks/24_publish_maps.ipynb

Once the map has been created, the map widget will be in your datapane account along with a code snippet for imbedding in html!

I noticed that the link you sent is using GEE in the Java environment, so this answer would require you to engage with the Python API, however I have personally hosted interactive maps this way and it is fairly simple. One caveat is that the maps will need to be re-updated every few days when the token expires.