i'm sure it is the same as a normal hard drive. Once the data is written, it is there.
There is a difference between written to the device and written in the persistent storage media. Both HDDs and most SSDs have RAM. The data only written to the RAM is vulnerable. HDDs which cache writes (and RAID controllers with the same tactic) can have the issue.
Most SSDs at the very least cache the metadata about the logical data block layout they present outside the drive. In the context of a write, the data may need to be stored in the SSD temporarily while other data is gathered to write the data out. In the gap, if the power is lost there can be an issue.
Some SSDs go to great length to always store the metadata on the flash media as it changes along with the data. Most "higher than average" priced SSDs have one or more capacitors on their motherboard to power the drive long enough in an outage to write the cached data to the persistent storage. Effectively they have their own built in "battery backup".
However, an external battery back just for the SSD isn't necessary in most situations. If are going to have frequent local black/brow outs the Mac's data/metadata is likely at just as much risk with a SSD as it is with a HDD. Same core issue of data/metadata being cached that hasn't made it all the way down the storage chain.
It is generally a bad idea though to just yank the power on a mounted and actively written to SSD drive. However, the same is true for a HDD.
The memory on phones and cameras are solid state, battery pulls dont erase stuff off the sd card.
It is not erasing stuff that is the issue. It is losing stuff that never was written. For example, if you take a high end DSLR camera with a buffer and start it shooting a max frame per seconds. Then while in that mode you yank the battery out while actively shooting.... you will likely loose the shoots that are newest into the buffer.
The upside for most phones and cameras is that is actually hard to yank the battery from them while they are actively in normal use. So the problem doesn't appear often. The firmware in the device will just quit if the battery power sinks below a certain level if loose power due to battery drain.
P.S. strobes presenting to the "surge protector+ battery back-up " as a brown out seems indicative that there is too much stuff plugged into the same electric circuit. An extension cord to a wall socket on a different circuit would probably work better for the more sensitive electronics.
