I reached out to Athom again regarding the issue (thanks @Doekse for clarifying this matter, and feel free to correct me if I am wrong).
The TLDR is that this is indeed a known issue and something that most likely cannot be fully fixed. The larger the Zigbee network, the more likely a Zigbee reset is required to get it operational again.
The longer explanation: the element that is causing the issue is the Zigbee routing table Homey maintains of your Zigbee network and connected devices. Apparently this table is stored in the Zigbee chip itself and cannot be accessed by the Homey OS. As such this routing table is not included in the backup nor restore of your Homey.
The consequence is that, after the restore, your new Homey first needs to rebuild that table and remap your Zigbee network. The problem is that while Homey tries to do that, Zigbee devices might flood the Zigbee network trying to find the old Homey/the old Zigbee coordinator. This excessive communication prevents Homey from repairing existing, adding new Zigbee devices and rebuilding the Zigbee network. The larger your Zigbee network the more prevalent this issue is and the less likely that Homey will succeed in rebuilding the network. For smaller networks, you might be lucky that Homey is able to rebuild its Zigbee network.
Though Athom indicated that they might be able to enhance the restore/rebuild process, it would not be a definitive solution for larger Zigbee networks. The only remaining option is to reset your Zigbee network on the new Homey and repair all devices (via the Maintenance > Try to repair option).
