"While holding down the A3, C#4, and E4 keys, set the [ ] (Standby/On) switch to On ( ). This activates Advanced
Settings mode."

That is correct. What you do next is critical.

In this mode, all of the [TYPE] lamps light are supposed to be up, and you can change parameters by using the keyboard, but the lights won't stay turned on and I'm unable to change the midi channel.

Yes, all the selection lamps come on to signify you have entered the mode where you can change settings.
You seem to think the lamps need to stay lit, that is not the case. Lights will flash to indicate data entry.

Hold the lowest C# and tap the Note that sets the Transmit Channel you desire.
_ Example: The lowest C# + C3 shuts MIDI Transmit = Off
The lowest C# + C#3 = Ch1
The lowest C# + D3 = Ch2
and so on...
When you have released the keys, all the TYPE lights will light to indicate the setting has been registered.

Hold the lowest D# and tap the Note that sets the Receive Channel you desire.
_ Example: The lowest D# + C3 shuts MIDI Receive = Off
The lowest D# + C#3 = Ch1
The lowest D# + D3 = Ch2
and so on...
When you have released the keys, all the TYPE lights will light to indicate the setting has been registered.

As soon as you press the two data entry keys, the channel is set.
After the lights indicate the setting has been made you can Power down and back on to exit the settings mode.
The Channels you set will be the Transmit and Receive Channels until you change them...

This setting applies to both the USB-MIDI IN/OUT and the 5-pin MIDI IN/OUT ports on the breakout cable.

Thank you so much for the quick and detailed response!
I understand I got it wrong by thinking the lights are supposed to stay lit, but if I understand correctly, they are supposed to blink like they do if I for example turn on the cp while pressing on C4 to do a factory reset. the thing is, when I hold down A3, C#4, and E4 while turning on the cp, the lights don't blink. That makes me think I did not enter Advanced Settings mode.
Is there a possibility that maybe the updater did not work?

Is there a possibility that maybe the updater did not work?

Once you do the firmware update, continue to follow the firmware updater document, which tells you how to verify the firmware version.

It worked!! Thank you so much for your help!

You’re quite welcome! Thanks for your participation and being a Yamaha customer!