I've seen this question asked, but there's never an actual answer posted. I replaced the battery in the Key Fob b/c it said battery low. Yes, correct battery CR2032. However, the car still shows the same error, and the lock function does not work, and you literally have to push the start button with the key fob for it to start. Oh, 2020 CX-5
Has anyone found a fix for this?

 

I can't find anything concerning this on the forums or on Mazda's tech bulletins, but that is not unusual.
I got the same warning intermittently with my 2020, but it went away after I replaced the battery, which I did it last week.
So much for the 3-4 year average FOB battery life.
Having to use the FOB on the start button generally means the FOB battery is no good.
Not saying that is your issue, but "new" batteries aren't always "new"., I'd try another battery or even a different brand.
It's not often, but I've come across "a new battery" being a "dead battery" multiple times in my years on the planet.
And somehow, they are most always at inopportune times
Let us know what you find out.

 

Not sure about the USA, but there is a service bulletin in my country regarding remote issues like yours.

 

There is a way to reset your remote, if it is within reach of the car too long. It is in the owners manual.

 

Where did you get that idea from? Certainly not from Mazda, the following is from my Owner’s Manual:

 

Regardless of what the owner's manual says, normal key FOB batteries last 3-4 years you can get that info just about anywhere.
It all comes down how you use them (functions) and how frequently.
I never replaced the one in my Honda CRV (had it almost 6 years) or my Honda Accord 5 years and it had remote start as well.
It could have something to do with original battery Mazda uses as not all batteries are equal when it comes to life span.
I used a Duracell this time, I'll see how it goes.