Dead battery - charging confusion

Hi everyone

Disclaimer - as will soon become apparent, I am a motorcycle thicko.

I bought my first bike - a BMW G650GS Sertao - about 4 or 5 years ago. It's been almost faultless in all that time up until I let is sit for 4 months over winter without riding it. I started it up briefly about a month ago, but life has gotten in the way again.

The battery, as you may have guessed, is now completely dead. There was a flicker in the display when I turned the key, but that was seemingly it's last breath.

I have tried to bump start it without success. The battery is probably 3 years old. I do a max of 2,000 miles per annum.

Please could someone advise what my best / quickest / cheapest cause of action is?
Should I buy a new battery?
Can I charge it / jump start it using a car charger?

My other bit of cluelessness....I have a lead protruding from the battery as per the attached photo for the trickle-charging - can I buy a motorcycle battery charger that fits this and plug it in to give it some charge, start the bike and solve my problems, or would that not work for a battery that is completely dead?

Does this trickle-charge lead only fit a specific trickle charger and how would I find out what that is?

As is probably apparent from this note....your help is needed....and much appreciated!

Cheers

Tim

3 yrs old and essentially dead probably easiest to replace it

Tayna batteries are the cheapest IME but go through the entire list available (they try to push you to an expensive one first) look at the AH and CCA I suspect sub £40 posted

Plug looks like an optimate one.

I’d put a new battery in and put it on the charger once a month going forward.

You might get away with charging it but a flattened lead acid is hard to trust again.