Did you earth the foil, possibly turning it into an even bigger antenna? I know the concept of a Faraday cage sounds attractive, but it has to be fully enclosed to be effective.
Microwaves obey the laws of light more than gravity according to my dad, when we bought our first microwave and mom was worried about all the torrent of bad microwaves rushing out, dropping to the kitchen floor, and cascading across the room when she opened the door, causing us foot cancer. This is what our neighbour had told her over the back fence. This was before COVID, MAGA, or even FaceBoob were invented. Some things never change!
Does it only fail when the microwave is actually heating (a critical door seal failure you should immediately fix as all microwaves should be contained inside the unit and none escape)? Just turned on and idle (possibly related and should be attended to urgently as there are thousands of volts floating around inside the cabinet, ready to spark and catch fire at even a hint of dust or moisture buildup)? Just turned off at the power point (definitely something else then), or the metal case on your microwave is reflecting interference to your Shelly from another device? Moving the microwave to another room or across the room make any difference? Turning it sideways (pointing the ‘death rays’ somewhere else)? Putting a small knot in the power cord change anything (sort of a coil filter that sometimes makes a difference at RF frequencies)?
Can you display the connection strength (in db) on your Shelly, or the router it is connected to? What is it? Does the error log show frequent WiFi disconnections, or device reboots?
Is MQTT configured correctly? Keepalive settings correct? There may be buffer space issues rather than connectivity issues at work here.
Unfortantely the only reliable way is the process of elimination. Remove anything that could possibly be causing interference and observe what happens when you add them back.
How many BLE devices do you have? How many devices overall? How many WiFi devices? Do they need to swamp THIS device? They use similar 2.4Ghz frequencies as WiFi and could be contributing to overall background noise. Are they also having reliable connectivity issues?
Just adding a larger antenna may not solve your problem that might be a strong source of interference will now swamp your device so it cannot connect, even intermittently.
Tools such as Android WiFi Analyser will identify neighbouring routers and busy channels. My neighbours have been caught out reconfiguring their routers for higher transmission power, swampimg the neighbourhood, and of course their own devices that cannot get a word in edgewise.
Check you also have the latest firmware on all your devices as often vendors fix things behind the scenes that are design oversights, and don’t mention them in their release notes.
Is your router firmware up to date? Does it support too many devices? Is the router system log showing frequent errors? How far away is your Shelly device? Do you have any repeaters?