and to prove their uselessness

You can see that the _osm_location cookie is updated. This cookie, despite its name, also stores selected layers. If you remove some event listeners, the cookie won't be updated on these events.

If you do map.off("layeradd layerremove") then after changing layers, going to some non-map-view page and going back to the map you'll see that your choice of layers wasn't remembered.

The problem is that those layer events happen probably more often than originally anticipated when the data layer is enabled.

What if we add a layer type check to the handler for which the handler was triggered? Something like:

map.on("moveend layeradd layerremove", function (e) { 
   if (e.layer && !L.TileLayer.prototype.isPrototypeOf(e.layer)){
	  return
   }
   updateLinks( 
     map.getCenter().wrap(), 
     map.getZoom(), 
     map.getLayersCode(), 
     map._object); 
  
   Cookies.set("_osm_location", OSM.locationCookie(map), { secure: true, expires: expiry, path: "/", samesite: "lax" }); 
 }); 

In practice, this does not give an increase, since this is not the only handler :\

Maybe listening to "moveend baselayerchange overlaylayerchange" is going to help.

This looks better, but will need to be fixed too.

And also understand how to track changes in the active object, which should be updated in the link of the OSM editor open button, which the updateLinks function does

Isn't there a way to pause events while the Map data layer is being rendered? https://github.com/openstreetmap/leaflet-osm/blob/ebfaf22426c265aaf3f401d70ffd02ca920623c9/leaflet-osm.js#L107

By the way, since you're looking into map data layer performance, we're also spending some time in XML parsing (DOMParser.parseFromString). Maybe we could switch to /map.json and directly parse the response as json(). Both Rapid and iD are using json for performance reasons.

parse the response as json()

This is not necessary yet. I have increased the limit of the maximum number of nodes for the local openstreetmap-cpimap, and I can say that parsing XML, which is 50 MB in decompressed form, only took 2 seconds. However, it took 10 seconds to download.