I ordered a bunch of capacitors to replace all of them on the defective PSU. Mainwhile, I did not want to wait. So I ordered a replacement power supply from ReactiveMicro. The original PSU will be restored, but… not for now.
The new PSU arrived today and was installed in minutes and the Apple IIe is working fine now.
The next project is replacing some of the keyswitches which are not working well. First I will try a cleanup, but for as far as I can see now,a replacement is in order. ebay, here I come.