@woozle I have added all device MAC addresses, including the WR840N, to the Allow List on the Archer C80 router. However, despite this, the WR840N still cannot connect to the network when Access Control is enabled.

Are there any other settings that could be blocking the connection, or what could be the cause of this issue?

  @Netwixell 

The WR840N in range extender mode has most likely a second MAC address that you are not seeing in the client list of your Archer C80 router.

Do you see a MAC address in your Allow list that looks like the MAC address printed on the label (bottom side) of the WR840N, with only the last number being different?

  @woozle Before adding the WR840N router's MAC address to the Allow List on the Archer C80, I disabled Access Control. After connecting the WR840N to the Archer C80, I checked the list of connected devices. In this list, there were two devices: my laptop and the WR840N. However, the MAC address of the WR840N is different in the first two characters from the one shown on the device itself, while the remaining characters match.

  @Netwixell 

Ok. So it looks like the MAC address you have already added to the Allow List is the "virtual" MAC address of the WR840N when it's operating as a range extender.

I think if you now also add the "real" MAC address of the WR840N to the Allow List, then it should work.

A Wi-Fi router usually has several MAC addresses (e.g for WAN, LAN and perhaps another one for the Wi-Fi radio) with the one printed on the label being any one of them.

I'd say you try the one printed on the label first.

You should be able to see all the MAC addresses of your router in the "Status" menu of the admin GUI. 

  @woozle Alright. I will do this and monitor the situation. If tomorrow the WR840N is still unable to connect, I will write about it here. I also want to mention that when the WR840N cannot connect to the Archer C80, I can enable the WPS switch, and then the WR840N is able to connect. In this case, I only need to enable the WPS switch. I don't need to perform the steps described in points Method 1, Method 2, and Method 3.

  @Netwixell 

I have no explanation for this. Normally the state of the WPS switch should not affect the general behavior of the router.
 

  @woozle Yes, it is indeed strange. But this is what's happening. Alright, so I will keep observing the situation for now.

Alright. So at this point, I can confidently say that the actions I took did not help.

This problem still persists.

  @Netwixell 

If it still doesn't work, then perhaps the TL-WR840N uses the so-called "many-to-one" mode and you can't use Access Control with it.

I can only guess, because I don't own a TL-WR840N, but you are able to see all the MAC addresses of your devices and with the help of the TP-Link article for which I already posted the link earlier you should be able to determine what mode the TL-WR840N actually uses.
https://community.tp-link.com/en/home/kb/detail/412804