You should decide on pk or use rms for real power, don't let us guess.
Magnetizing current for coupling may need to be about 10% of real current.
Allow Rs on coils to cause 10% loss at full load for VA rating.
Can you use 1:2 centre tap secondary?
You know how to compute X
L(f) right?
5 V / 1 A = 5 Ohm
X
L (30 kHz) = 50 Ohm, L = 265 uH
DCR << 5% of 5 Ohms = 250 mohms
This one is not quite big enough for L but is a good starting place to look. $9 at D-K
View attachment 186672
Getting closer using this search method
https://www.digikey.com/en/products/filter/specialty-transformers/165
View attachment 186673
You can wind your own or modify this to isolate the secondary. You only need 3 windings and 6 pins , but your configuration is uncommon.
but it meets my specs. 1:1:1
L p1-2 : 269 uH vs spec 265 uH
DCR 150 , 200 mohms vs spec 250 mohms max.
View attachment 186674
$172 per 100