I have the same issue after the update to 13.4.1 on my 16inch M1 MacBook Pro 2021. The primary click stopped working and restart didn't help. I restarted in recovery mode where everything was normal and proceed to reboot again when it momentarily fixed the problem until it came back again after a few minutes.
I called the apple support and they suggested to reinstall Mac OS from recovery mode. I did and it started working again however, it is intermittent. Read below behaviour post reinstall:
I have noticed that I can reproduce the problem by letting the MacBook sleep on its own due to inactivity. As soon as the display goes off, I press the click to wake it up again and the problem comes back. Note that you have to wake it up quickly otherwise if you leave it for more than a few seconds before waking it up again, it goes to the password prompt and not sure if it is reproducible that way.
Once it gets into this state, I have noticed that it fixes itself after leaving it for a while or restarting in recovery and then full restart. This is really disruptive and I have read some reddit posts where I am sure I am not the only one with this issue. Please fix or escalate.
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