The lenses were both set at f4, the 'sweet spot' (apologies to anyone offended by this

) on the aperture ring and left there when fitting the TC, thus my reply to the OP.
Fair enough... I forgot about manual lenses with aperture rings.
The sweet spot on the lens is because of the physical properties of the closed aperture blades at the set aperture, the "new Aperture" reported in tthe camera is because the TC is absorbing some light so affecting exposure fooling the camera computer to thinking a smaller aperture is set it isn't physically changing the diameter of those aperture blades. Therefore I submit thet the "sweet spot" of the lens is still the same with or without the TC.
The sweet spot is because the aperture restriction is eliminating (blocking) light from the periphery of the objective element, which is not as well corrected for spherical aberrations; and so improves image sharpness/quality. But stopping down the aperture also increases diffraction, which degrades sharpness/quality. The sweet spot is where the improvement gained is greater than the degradation caused.
A telephoto converter is exactly that. It is intended to
convert a non telephoto lens design into a telephoto design; which is why it works best on prime lenses (non-telephoto). And it works exactly the same way a telephoto lens does; the rear telephoto elements magnify the image circle. The magnification spreads the light out, which reduces the light intensity and exposure. And while the aperture restriction hasn't changed, it's size relative to the new focal length has; and therefore the combination has a larger minimum f#.
I.e. a 300mm f/2.8 lens with a 2x TC attached is not "behaving like" a 600mm f/5.6 lens. It
IS a 600/5.6, only that it is physically shorter than it otherwise would be (telephoto).
The combination is a
new lens design and therefore the sweet spot may change... individual testing should be done if it is of concern. And you might want to test multiple TC's as well; you can get into a situation of compounding errors (usually), cancelling errors (theoretically), or neutral (if you're lucky). Nikon did this for the older 800/5.6, then they sold the TC with the lens and with a matching serial number (that's the main benefit of built in TC's today).
FWIW the same shots taken with just the lens but cropped to the same image proportions looked just as good as either TC
That is often the case, or nearly so; especially with today's high resolution sensors. Magnifying the image circle results in a reduction of recorded/total detail much like cropping does; the only difference is which factor limits the resolution more (lens/sensor).
If the lens can resolve far more than the sensor can record, then degrading the lens' resolution with a TC isn't a problem; but degrading the recorded image resolution instead (cropping) would be... this was common back with ≤12MP FF cameras.
Conversely, if the sensor can record (nearly) everything the lens can resolve, then degrading the lens' resolution would be a problem; and cropping would not be... this is more common with 20+MP cameras today.
Not sure why I felt the need to explain all of that...
