It helps to know the make/model of power supply. Is there a fuse on the DC side?
When power comes back on, the battery will draw high current charging but the PSU should not go into hiccup mode I think.
The PSU is too big at 8A for a 7Ah battery, that can be dangerous. There are also PSU's designed for 12V battery like Meanwell
LAD-120AWhat I do is use two isolating diodes plus a PTC fuse to limit charging current, and a fuse. I'll add a schematic later.
edit: added schematic of what I am presently using.
I find with old SLA batteries, one cell shorts so you have to limit charge current or the battery melts. This is a danger.
I was going to use a 4Ω 5W resistor but that is big and can be a lot of heat. Goal was C/10 max.
The
RXEF030 polyfuse resistance limits charging current, at the expense of recovery time charging.
Of course it usually trips during higher charge currents but as the battery charges it holds around 0.3A, it eventually cools down and resets.
You could use a dual Schottky diode in a TO-220 package. Silicon Vf is over twice the heat.