How to determine the nominal current of an LED?

It has several unmarked white SMD LEDs ...

... without marking you cannot get a datasheet and without datasheet there you don't have a chance of finding out the real current.

However there is a possibility of getting a rough impression of the current needed by the LEDs:

Attach a current source and a voltage meter to the LEDs (the current source may be a voltage source with a resistor in series).

Slowly increase the current from 0A until the product of current and voltage is the power you estimate (the nominal power of the bulb multiplied by the efficiency of the transformer; maybe 5W for a 7W bulb).

VERY approximately:

LED power rating = bulb_ratinf/number_of_LEDs. So if eg 5W bub with 15 LEDs.
LED power ~= 5W/15 = 1/3 Watt per LED.
LED forward voltage is typically ~= 3V.
So LED current ~= LED_Power/3V = 0.333/3 = 111 mA.

This should not be too far from "about right".

Bulb Wattage ratings are expected to be ~= LEDs DC Watts in.

Modern white phosphor LEds usually have quite a low ratio between
i_operating_max_typical and I abs_max - often in the 10% - 20% range.
LED lifetimes increase for I_LED < Imax and usually are acceptably affected for I_LED > Imax by a moderate amount. Operating on the conservative side seems wise.