Nice project

manufacturers datasheets, RF appnotes etc all mention this, with results for different usecases (like gnd plane size etc). I mentioned it a few times on the forum:

• nothing under or near antenna (keep out zone)
• their matching circuit, and CE/FCC certif are based on their development boards+their antenna if external, often without enclosure.
• there are a very few pcb antennas which are resilient to untuning. ceramic or meandered pcb are usually more compact but less resilient (like when you approach your hand and device suddently has better or worst communication)
• once you change any of these parameters (board shape, gnd size, enclosure etc), it breaks FCC, and may need retuning, still you can get useable range.
• "ideally" tuning should be done once enclosed for example. manufacturers can't cover all cases.

on my side, I try to follow these rules. and when interested in a design or a device, I check this. Mainly the routing+gnd, antenna choice, keepout zone, and orientation vs my usecase (long range needed or not for example)

Normally the antennas are tuned for "no cutout" but also no GND-Fill. The datasheet gives some info: "... It is necessary to ensure that the antenna is exposed, preferably vertically upward"...avoiud traces underneath the module."
With the SMD-modules of the nrf24l01 I tried the 3 options: No pcb, with empty pcb and with traces and gndfill (f*ckup on my part).
Results where: No difference with no PCB or empty PCB, Superbad with traces or GND Fill.
The PCB-trace antennas are much more effected by traces and cables in the vicinity.

Some manufactureres even specify detailed the PCB zones. Check the Bluegiga BLE121LR Datasheet Page 23 for some nice graphs and pictures.
This considerations should also apply to other 2.4ghz antennas (not pcb-antennas). So Maybe a GND PLane with via stiching?

https://www.silabs.com/documents/public/data-sheets/BLE121LR-DataSheet.pdf

I wonder whether removing the PCB that lies directly under the module's chip antenna (not on the module, of course, but on the PCB that the module is soldered to) would improve range/coverage? I notice that some of the projects do this, and others don't.