Plain folium + Earth Engine getMapId tile layers. Build a folium map directly and add each EE layer as a tile layer from its map-id URL.
Tile URLs from getMapId will expire in about a day; regenerate the map to revisit later.
Note: map_id_dict['tile_fetcher'].url_format might contains unformatted placeholders (like {state.tile_base_url}) which break Folium. Instead, construct the URL manually: url = f"https://earthengine.googleapis.com/v1/{map_id_dict['mapid']}/tiles/{{z}}/{{x}}/{{y}}"
Use a basemap. Add it as the base and hide it from the layer control.
Save an .html file and open it.
Optional Python Server (for dynamic pixel values): If the "Pick coords" tool needs to show actual Earth Engine layer values, serve the map using a Python http.server backend with a /value endpoint. The map's JavaScript can then make fetch() calls to query EE dynamically (e.g., via ee.Image.reduceRegion).

Basic Controls (more can be added)

Per-layer opacity sliders, embedded in each layer-control row (Code-Editor style): tag each EE layer with a CSS class, then on page load add a range slider to every overlay row that sets that layer's opacity. Note: Folium-generated TileLayers do not have a name attribute in their Leaflet options, so you cannot match layers by name. Instead, extract the internal layer ID directly from the checkbox element (var layerId = input.layerId;) and adjust its opacity using map_instance._layers[layerId].setOpacity(op);.
Clear all / Show all buttons, placed next to the layer control. Implement by clicking each overlay checkbox through Leaflet's own handler so layer state stays consistent (and layers can be toggled back on).
"Pick coords" toggle (off by default): when on, the cursor becomes a crosshair and a map click drops a lat/lon popup; when off, clicks just pan. Grab the Leaflet map instance from the page's globals and gate the click handler on the toggle.
Disable click/scroll propagation on custom controls so interacting with them doesn't pan the map.

Layer design principles

Categorical / raw-class layers: remap class codes to contiguous values and apply a palette; put the class order in the layer name so the name doubles as a legend.
Reference boundaries (lake polygon, AOI, admin) as styled outlines with no fill, on top.
Optical true-color backdrop (e.g. Sentinel-2) for human context under the overlays.
Offer the raw underlying layers (each product's full class image, unmasked) as toggles: they're the real verification tool when a derived layer looks wrong.