Modern Vespa

Hi, im new here and looking for any suggestion of what might be my problems here before spending more money.

Few days ago my BV350 started losing power. That would come in short bursts while going 50-80kmh. Spark plug and cap changed, nothing.

Today after starting and idling for 20secs. It died/cut off the engine when i rolled on a bit of throttle to get going.
After reseting the start button does nothing. I cant even hear selenoid statt relay clicking. Absolutly dead.

Battery shows its at 12.2V and all the lights light up when key is turned.

Is it possible that all of these problems are caused by a faulty battery? Maybe a dead cell?
If you need any more info about the scoot im here

Thanks for suggestions

Also i would add. Idle was uneven today when it started before it shut off when i applied bit of throttle. It sounded like it was gonna stall/shut down for a few seconds.

12.2V is very low for a battery - at rest a good fully charged battery should read 12.6V for a sealed or gel battery, and 12.8V for an AGM

Test the charging system:

Diagnosing Charging System Problems

Quick update. If i ignore the not working "start" button and i jump the bike. It gives absolutly 0 spark! Tried also with ht cap and soark plug off, nothing.
ECU seems to read the key as immoblizer and everything else turns on.