I have a normal ap-station setup, but sometimes I want to extend the signal. I understand that if i were to put a repeater and use the same band in the repeater for receiving and transmitting, I would halve the bandwidth, so to avoid that I would need to use a dual-band setup, where I could connect to the backhaul by 2.4 GHz and then to the station bridge with 5 GHz.

I have the following setup:
Is this feasible to extend the range? How would I make that configuration, do I make one radio in the netmetal be 2.4 on "station bridge" and the 5GHz one "ap bridge"?

This is feasible way of doing it.

As to wifi radio modes ... it's up to you, constraints are:

• both AP and station have to run same generation of drivers (wifi or wireless), mixed drivers are not compatible in station-bridge mode.
  Since each device can only run one generation of drivers, in case depicted by diagram this means that all wifi devices have to run the same generation of wireless drivers.
  Running different generation of drivers on adjacent devices means limited transparency of that particular wireless link and that creates a division in your network. Which might not be catastrophic depending on high-level expectations/requirements ...
• one of devices, forming "wireless bridge", has to be in ap mode (can be ap, ap-bridge or bridge, depending on driver generation and desired functionality), the other in station-bridge mode.
  Selection of which should run in one of ap modes is more or less arbitrary. But if you want "the left side" (the one closer to router) provide wifi access also to "normal" clients, then that's the side which should run in ap mode

So ideally the left netmetal would run 2.4GHz radio in station-bridge mode and 5GHz radio in ap (wifi) or ap-bridge (wireless) mode and both wifi/wireless interfaces would be members of same bridge. The right netmetsl would run 5GHz radio in station-bridge mode and 2.4GHz radio in ap mode, again both wifi/wireless interfaces memvers of same bridge.

Frequency on 2.4GHz radios should be carefully planned so that right netmetal doesn't interfere with hAP ac3 2.4GHz signal at left netmetal location.

• both AP and station have to run same generation of drivers (wifi or wireless), mixed drivers are not compatible in station-bridge mode.
  Since each device can only run one generation of drivers, in case depicted by diagram this means that all wifi devices have to run the same generation of wireless drivers.
  Running different generation of drivers on adjacent devices means limited transparency of that particular wireless link and that creates a division in your network. Which might not be catastrophic depending on high-level expectations/requirements ...

What do you mean by "the same generation of drivers"?

To be clear, there will be a client device connected to the right-most netmetal. There won't be any other client devices connected to the repeater, so I just need the client device connected to that rightmost netmetal to have internet.

What do you mean by "the same generation of drivers"?

Either legacy wireless ... which is required on older generation of hardware, up to and (mostly) including AC.
Or wifi (in particular either wifi-qcom and wifi-qcom-ac) ... which is rewuired on newest generatiin of devices ... AX and some AC.

The consideration of driver generation is only important for the radios running in station-bridge mode ... normal clients can work with either.

What do you mean by "the same generation of drivers"?

Either legacy wireless ... which is required on older generation of hardware, up to and (mostly) including AC.
Or wifi (in particular either wifi-qcom and wifi-qcom-ac) ... which is rewuired on newest generatiin of devices ... AX and some AC.

The consideration of driver generation is only important for the radios running in station-bridge mode ... normal clients can work with either.

Can I use an older driver on, say, netmetal ax, so it's compatible with, say, groove A 52?

All AX devices must use wifi-qcom