I'm assuming your single pole switch has the internal illumination wired across the switch terminals. When the switch is 'off' the internal illumination bulb is in series with your led porch light. Their respective impedances dictate what voltage exists across the switch compared to that across the led porch light.
When you put a filament bulb in the porch, which is low impedance when it's 'cold', effectively all the voltage is across the open illuminated switch, so the switch illumination bulb will be at its brightest. This is how it is assumed that some illuminated switches will be used.
When you put an LED bulb in the porch light, obviously that will draw a lot less current than the filament bulb. The behaviour of the LED bulb in series with the source of illumination in the switch will depend a lot on the wattage and characteristics of the bulb, and also the type of illumination source in the switch.
I think it's fortunate that your LED porch light doesn't flash rather than glow.
I notice that the blurb on Amazon UK for the switch you gave a link to says "This switch is compatible with incandescent loads only and is not recommended for use with LED or CFL lamps."
One possible solution might be to fit a snubber (series capacitor and resistor combo) across your porch light connections.
Purchase RC Snubber from the only Shelly authorised reseller in the UK. Shop Wi-Fi smart home automation now!
shellystore.co.uk
(sorry - link to a UK site)
Re your last query, if you put a motor or similar (which I guess you're not actually going to do!) in place of the porch bulb, then the small current that powers the switch illumination would flow through the motor, but likely wouldn't actually move it!
Similar to you putting the filament bulb in!