I know the full diagram, I once had a KWS1, by when moving had to sell it

The signal from the FL101 filter has a max of 1.5 Volts when whistling in the microphone. for CW you need to inject approx the same level 250 kHz, so not really piss weak. Low voice SSB from the filter is, a few tens of a volt.
The mixer does have gain, so if the tank is tuned well, you can expect a few volts upto 10 Volts RF at VFO + 250 kHz.
Indeed this kind of mixer does not balance the input away, so there is a trap needed for the VFO frequency to attenuate that frequency at the output. That is the left part of the tank circuit.
When you don't find that signal, the tank is not tuned or the tube is bad.