If you mean how you can check if FortiGate is doing Deep-inspection on traffic and able to inspect full traffic, then in logs, you will not see any explicit flag. You can check which firewall policy was matched and see if deep-inspection profile is used. Best way how to check if FortiGate is doing inspection is to open HTTPS website and check who signed the certificate. If you will see that the server certificate was signed by CA that is on FortiGate, then full inspection is happening.
But I want to see why my IDE or Antivirus or other tools are not working anymore after enabling full inspection. There is no way to check this in the gui why my Bitwarden installation fails when do download start. There is just a general error msg.
Or Iframes on a website which are not shown correctly.
That's why I want to see which connection is decrypted to get an ideo which URL/IP addresses are to whitelist.
Some applications have problems with deep-inspection especially if you have self-signed CA on FortiGate and some FortiGates might have it's own cert store but you might want to double-check that your PC has this CA installed as trusted root CA.
My suggestion would be if it is known application, you can use ISDB or fqdn to exempt traffic from inspection.
Unfortunately, FortiGate does not have this kind of flag. Each log will have policy_id that traffic matched and this can be used to check if deep-inspection is applied. But even this does not mean that deep-inspection is always performed, because maybe traffic is exempted or using non-standard port, etc.
For the Fortimanager and Fortigate communication, you may consider to create dedicated policy for this and do not apply any security profiles since it is a trusted IP. You may set specific port number if required.
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