Thank you @msfujino for your kind comments.
Some tests suggest that your hypothesis may not apply in the particular case of the FM8625H on the XIAO.
Average RSSI during some tests:
Test 1
Both I/O Pins in INPUT mode ()
no external antenna: -64.6
with external rod antenna: -55.9
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Test 2
VDD I/O pin in INPUT mode and VCTL I/O pin is LOW (OUTPUT mode)
no external antenna: -66.0
with external rod antenna: -56.0
Test 3
VDD I/O pin in INPUT mode and VCTL I/O pin is HIGH (OUTPUT mode)
no external antenna: -66.6
with external rod antenna: -56.0
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Test 8
VDD I/O pin is (OUTPUT mode) and VCTL I/O pin is LOW (OUTPUT mode)
no external antenna: -47.5
with external rod antenna: -51.8
Test 9
VDD I/O pin is LOW (OUTPUT mode) and VCTL I/O pin is HIGH (OUTPUT mode)
no external antenna: -68.7
with external rod antenna: -44.8
As can be seen, when the RF switch is not enabled, the RSSI is about -66 when no external antenna is connected to the XIAO and it is about -56 when an external rod antenna is connected to the XIAO no matter the state of I/O pin 14.
Is it meaningful that the presence of an external antenna actually degrades the performance when the RF switch is enabled and the internal antenna is selected while it helps when the RF switch is not enabled?
Truth be told, this is way outside of my knowledge set. You may wish to check the code on GitHub and run the tests in a different environment to see if that yields different results.
Thank you very much for making sense of antenna circuit on the XIAO and many thanks to @fons for pointing me to this topic. I learned one important lesson: turn the RF switch on.