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It's on the *modal* that appears when enabling dog mode. It's also on the Tesla support site:
"Note: Dog Mode and Sentry Mode cannot be active at the same time."
https://www.tesla.com/support/car-safety-security-features
Same issues here. 12 Pro on ATT 5G. I tried logging out of the Tesla app and back in but got this error. Then I connected to VPN and was able to sign in. But after disconnecting from VPN, I get network timeout eventually again.