Challenge accepted!
RP2040 Supermini board $1.79
0.96in OLED display $1.99
Si5351a board $1.39
Free shipping if buying all 3 together
Some tax (which may rise quite a bit soon).
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Total $6 or so. I bought all these parts from Aliexpress before, no issues (unlike their fake transistors).
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Other parts: small prototyping board, test socket, 1N4148 diode detector, few resistors and capacitors to make a simple amplifier around the DUT, USB cable for power (and maybe sending the data to the PC, then no display is required).
The software should be trivial: sweep the frequency, measure the rectified output using the ADC, find the point where the gain drops by some amount? (say, 6dB), extrapolate fT. Arduino IDE or MicroPython, your choice.
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I don't expect to get to it until? the next weekend, but it should take me about an hour to build and a few hours to program.
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The same thing can be done with NanoVNA, but there is less fun doing that (and more initial investment in case you don't have it yet for some reason).
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73, Mike AF7KR