Shimano Lever leaking oil during bleed

First time attempting a brake bleed, sorry for any wrong language.

My wife bought an electric bike with one brake missing a bleed screw on the lever and totally lacking oil.

I bought a new screw and a bleed kit, and I've managed to attach the syringe and pump in some oil.

However, as soon as oil appears in the funnel it starts leaking out from the side of the lever until the funnel is empty again. The funnel is definitely screwed on properly, the oil is not leaking from where it attaches but rather the large four-quadrant hole on the side.

Is this normal? Do I need a new lever? Thanks for any tips.