If you have an audio generator and AC voltmeter you can resonate the winding with a capacitor to get an idea of inductance. It's small signal so full run voltage inductance in lower.
High voltage winding magnetizing inductance is probably in range of a Henry.
Secondary winding is fraction of Henry.
Leakage inductance with low voltage winding shorted is a few milliHenry.
Select an approximate cap value based on resonating near 50 Hz. Put a series cap in audio gen fed that is less then 1/10 the resonating parallel cap value to keep loading on winding low. Place high Z AC voltmeter across winding and adjust audio gen freq to peak AC voltage across winding. Back calculate inductance based on actual resonate freq with cap value used to resonate. If resonance is less then 30 Hz or greater then 70 Hz readjust the parallel cap value selected to get closer to 50 Hz resonance.
Measure series resistance of primary, series resistance of secondary, magnetizing inductance (no load on other winding), and finally leakage inductance. In your case, the high voltage secondary leakage inductance is important (shorting low voltage side) as it will represent the series inductor in the output high frequency L-C low pass filter with just a parallel cap on secondary.
On the final cap selection for filtering, make sure you keep the parallel resonance with secondary magnetizing inductance much higher then 50 Hz. Not sure what a good target is but I am guessing at least 4 or 5 times 50 Hz. Getting close to resonance can cause high voltage to develope on output during light loading on inverter. Oil filled AC moter run caps are what you can use.
Commercial units like Outback FX series, or Xantrex XW series DC-AC inverters work with low freq transformer with high freq PWM MOSFET H-bridge input. They design transformer with compromised laminate core coupling to get a target leakage inductance.
Normally this is not what you do for a normal power transformer as leakage inductance is considered a bad thing.