Its strange that the log is not showing anything for the projector.
If the projector was not in the log then it implies then it shouldn't be an ssid/passphrase problem because the log should show a login failure.
When you looked at the log, did you just look at the default "error" listing? If so, change "error" in the dropdown box to "info" and hit apply and then check the log again.
The 5ghz is really irritating as its always hiding & showing itself for me as well.
I was going to suggest looking at the 3864 when the projector is connected to see what ip gets assigned to the projectors mac address, and then applying a static ip to match in the 5366, but would only be useful if the log indicated that there was a connection.
I had a Ubiquti AP before and the 5Ghz radio died and causing the connection coming in and out. However, it affect all the devices not just one in specific.
There are some members that found iCloud is saving the older passphase for a wifi network with the same SSID and not able to connect with the new modem/router. Not sure if xiaomi has a similar system. I know with my Mi5S, i need to create a xiaomi account to use its functions and it also saved my wifi network's details.
Have you tried, doing a hard reset on the 5366 and try to connect the project without any SSID or passphase change?
I think @SillyGogo may have provided a possible clue to the cause in his comment above. This could be a NAT Loopback issue which I understand the F@ST5366TN may not currently support (happy to be corrected if not the case) rather than a Wi-Fi connect issue. May I ask, did the projector come with a remote control and if so, did you use this to pair the projector to the F@ST5366 TN or are you using a cloud based App on your Wi-Fi enabled Mobile where you have a sign-in to your account on the Xiami Web site to set up the Projector?
Modems that don't currently support NAT Loopback will block connections where the Smart Phone is being used for set up and control when you are within your Wi-Fi Network. Hopefully future versions of firmware may address that limitation. I am unaware if this applies to the F@ST3864V3HP which appears not to have this limitation from your experience.
The connection path is like this - Phone App in home Wi-Fi zone to Cloud Based Server Log-In/Registration of equipment, Server then links to the Internet for connection through Modems' Firewall to the device that is being programmed through the App. This is called a NAT Loopback or Hairpinning the connection path as it goes out of your home and then comes back in. Generally when this feature is absent in the modem, people are unable to connect Smart Home Lights, Wi-Fi Security Cameras or see the security videos from their Phones when inside their Wi-Fi Network.
Also assuming generic User Plug and Play or UPnP has been enabled within the modem to allow registered UPnP external service providers to be allowed into the Modem to connect to their respective devices . I think the reason why your Hotspot experiment was successful is that the established path was set up by connection to your phone through the mobile network then back to your phone then to the projector, avoiding your Modem's Firewall.
I would like to give all of you a thumb up for your efforts in helping. Really appreciate.
I am not familiar with network wifi etc. I am a sort of understanding what you have described, but may be a bit difficult for me to setup the system if some further knowledge are required. I will have some tries later to see whether I can make it work. Currently, my wife has asked me to remove the F@ST3864V3HP connection as it looks massy and the Wifi network is a bit mixed up :-).
Yes, I am currently setup the WIFI for the proejctor with its paired remote control.
F@ST3864V3HP does not have this issue all the time I have used. And it still works perfectly (although it does drops frequently sometime).
I have reset F@ST5366TN, and it did not work.
Thank you again for your help.
Thank you for the feedback. If there is a development that introduces NAT Loopback feature into the F@ST5366TN, I will update this reply. Optus will automatically update your modem/s when it is on-line and it may require a restart to activate the new firmware. Handy for you to keep a record of current firmware status so that you know when things change. All the best.