This is a AC transfer relay circuit that transfers from 120V MAINS to battery backed 120V inverter when the MAINS fail.
Do you think it will be safe and reliable?
Please delete
No. You need a fullwave rectifier and a smoothing capacitor, to stop the relay from turning on and off at 60Hz or trying to.
I Googled the EE2-24NU.
https://www.mouser.co.uk/datasheet/2/212/KEM_R7002_EC2_EE2-1104574.pdfAssuming I've got the correct data sheet, the coil resistance is 2k88, so you need a 12k 1W resistor.
I think this is a penny wise, pound poor solution and it would be better to use a 120VAC relay, even if it's more expensive and through hole.
Another issue is the 00 uf capacitor on the relay coil. This will delay the relay drop-out time resulting is a delay before the inverter power is applied. Also the capacitor will cause a slow release which could cause some additional arcing as the contacts switch. Minimize the capacitor sizing by using a full wave rectifier and only enough C to eliminate buzzing.
paul