As mentioned above, router is ASUS RT-AX53U, not itself in your blacklist, but a likely close relative of Asus RT-AX58U. Nevertheless, such "incompatibility" seems a quite broad concept, for an intermittent problem, affecting different ESP8266 in different degrees. With some of them, not Shelly, I hardly had any problem. Conversely, this morning I decided to make a last factory reset in the Shelly EM (usual SSID, nothing changed in the router) and magically it started working again in http, the app, and home assistant, with no data gaps over several hours!
Next time I will first insist with factory resets, but I wonder if it is just the router to blame.
Thank you.