As someone who was literally just dealing with this with my '21 CX-5 Touring for the last several days and only managed to figure it out (for myself, at least) last night, let me ask you this: is this the only electronically controlled system that you are having issues with?
I ask this because this is how my issue started, but it wasn't because of any actual issue related to the EPB's mechanical functionality. For me, when my problems began, I too would get that message about the EPB malfunctioning, but it would go away after turning my car off and then back on, so I went about my business as usual and all was fine. I would just turn my car off and then back on any time I would get that message or the critical vehicle malfunction alert from the app (which was only going off because of the supposed EPB issue).
THEN, I noticed my car having some mild trouble with cold starts. She would start the ignition process, but it would take a second or two for the engine to actually crank and turn on. Any time this happened and it took longer than a second or so for the engine to start, the EPB light would start flashing and I would get those malfunction notifications. But after the initial cold start and subsequent "malfunctions", I would do the same thing I had been doing and turn the car off and back on with no issues whatsoever.
Eventually, after doing this for quite some time (which was quite stupid of me to have been doing, but I was still trying to work out what exactly the issue was), I started getting the check engine light coming on and sometimes the car would take a few tries to get started, but was still working fine. I found that if I turned it off and on enough times, the check engine light would also go away (usually after about six times) and everything was apparently operating normally. So I proceeded to continue my "method" for getting all the malfunction problems to disappear and, by this point (when I had been dealing with these problems for the better part of a month or so) I had a few ideas of what might've been behind the issues, but couldn't find any answers with any level of certainty and was trying to avoid a costly trip to the dealer... so I carried on.
One morning, I'm about to leave for work and the car doesn't start at all. I try a few times and nothing. When I got home, I spent the better part of the day (and night) with an OBD II scanner trying to diagnose what the issue was. Long into the process of doing this (and at about 12:30AM), all the electronically controlled systems in my car started going absolutely crazy and lighting up with malfunction lights going on and off each one repeatedly and then the car would start beeping randomly and uncontrollably. My brake had seized up, but it wasn't like I could even start my car at that point and, eventually, all systems on the car shut down, but I could hear them trying to come back on with only limited success and then the car would start beeping again. The electronic door locks wouldn't work and I ended up having to use the manual key inside the fob to get back in the car after going around and manually locking each door. Once that happened, I turned my full attention to the internet to try and figure out what kind of The Exorcist level possession I had just witnessed my vehicle have.
After scouring any and every forum and help page and blog post and help sites I could find (and armed with the knowledge of the error codes my car was throwing at the time of its possession), I settled on the general consensus' opinion of the issue stemming from the battery being drained (most likely due to some of the electronics having parasitic power draw once the car is off). So I took the battery out, went and got a new one from Costco, plopped it in and VOILA! She breathed life anew. All in all, the old battery removal and installation of the new one took me maybe fifteen minutes total, combined.
IF your issue is the same as mine (and I'm not saying that it is), hopefully my experience helps and saves you a lot of time and confusion after the ordeal I just had, as well as keeps you from having to go to the dealership, which I can almost guarantee would have cost me SIGNIFICANTLY more than what it cost me, which was only the cost of the new battery. If you have any questions, feel free to ask. Also, sorry for the outrageously long post!
Best of luck to you!