Thanks, I did some more checks: power supplies on the pins of the various devices were ok, clocks were also present (except the 32 kHz, I guess it's used maybe only for the RTC during power down?) but I saw there was practically no activity on any pin at power on.
Then I noticed that that the SDA line was stuck at 1 V instead of being at 3.3 V: the pull-up resistor was measured to be ok, so something was pulling that line low. I then compiled the DiSlord FW after commenting out the calls to i2c_transfer() for the Si/MS5351 and the AIC3204 and flashed the NanoVNA: lo and behold, the display was alive and showing the usual Smith chart. The device was anyway unresponsive, maybe waiting for data from the AIC3204.
So it seems that one of those two devices on the I2C bus likely died, how that could have happened I have no idea.
In hindsight, it seems a bit strange to me that the FW just hangs, without showing any error message anywhere, if the I2C communications fail.