Modern Vespa

Used previous day, ~40mile round trip.
Went to start it today and normal 'boot up' happens, gauges initialise, beep and lights on dash illuminate.
Put brake on and hit starter button.
Can hear it trying to turn over (whirring sound) but to no avail and just doesn't start.

I'm not a mechanic so have just been fumbling through various forums/vids to get an idea of where to go next.
Im thinking to look at the relay to the starter motor?

Will attach a vid of it's worthwhile??

Checks/background
Brand new battery installed to try address this issue.
New spark plug @5000miles.
All (11) fuses inspected and tested
Kill switch toggled(status seen on dash)

Doesn't get ridden in wet.
Stored in water tight garage.
~7500 miles (I purchased 2yrs ago with 4500miles)

Does the fuel pump run (look inside the tank) when you turn the key?

Ditto on pulling spark plugs to check for spark

Current state....

12.2v on initialisation, drops to ~11.5v when I try and start.

Removed spark plug, looks as per pic.

Connected it up, with the cap on as far as I could get it (pic)
I assume that is correctly applied.

I then placed the tip on the engine and tried to start it.
I have a video of this but can't upload .MP4 files.

I didn't see a spark so will be looking to get a replacement for this one (CR8EB)

Hopefully this is the issue but, a little weird since that plug is 2-3k miles old??

Also put a screw driver in the plug cap.
Turned it over and could see a spark against the engine from the screw driver, so I'm assuming the Coil etc is OK.
Fingers crossed it's just the spark plug, awaiting replacement.....

A spark is a good indication, but sometimes the spark plug is simply no longer good. Since you now see a spark, it is best to look at the fuel supply. If the engine has both, then something else is wrong. But usually it's fuel or electricity when the engine doesn't start.