I Googled the question, and could not find an answer.
I'm going to buy a product that has a remote.
I can choose a remote that takes an A23 battery or a 2032 battery.
An A23 battery is made up of eight individual LR932 alkaline button cells enclosed in a wrapper.
Since alkaline batteries leak, I am guessing that A23 batteries leak.
Is this correct?
(If so, I'll get a product with a remote that takes a 2032 battery.)
I’ve never had an A23 leak, per say. They do alright but all other things equal I’d take a lithium cell over one.
Okay, that sounds good.
I'll go with the lithium 2032. 
a23s probably would not leak - button cells usually do not have enough chemicals
plus they are all in a wrapper in case one did
BUT
i would go 2032 without question
batteries much more available and will never leak
also shelf life longer - important in a remote, they use very little energy
This is the item that I ordered...
https://www.amazon.com/dp/B07Y9RRWNB
It's a "remote control outlet plug."
I installed it and tested it today.
I have a router in my mom's room, and I'm going to use this remote control to turn the router off and on when I need to and she is asleep.
The remote control uses a 2032 lithium button cell.
It works fine now, but we'll see how long it continues to work. 
about 7 years would be my guess
Yes, they do. Whether individual or stacked doesn’t matter, the chemicals involved eventually corrode the case. Any steel case will eventually corrode including liion and nimh but alkaleaks are among the worst.
never seen a lithium primary [cr123a] leak
Yes they do leak, but since they are in a steel wrapper ( i assume you talking about 12v cell, that is used in old car key fobs) , chances of them damaging your device are almost 0
Definitely go with the lithium primary 2032. My previous comment was in regards to alkaline button cells.
2032s have been inside PC for a long time. I’ve been inside hundreds of them.
And replace many that have died. Often dead for years.
Nary a leak in sight.
All the Best,
Jeff