I've been spending a couple of months messing around with this absolutely insane top of the line Sony KW-36HDF9 from Japan. Shockingly for an HDCRT, Light guns WORK on it! It's entirely unlike anything we got in the USA in the 90s, or even the 00's. Even the PS5 and Switch work on it!

In case you ever find one, the calibration menu is accessible in a similar fashion to other Sony TVs. With the TV powered on but in sleep mode (power off, red light on):

Press in this order:
画面 表示 (Display Options)
5
音量 + (Volume Up)
Power

1 and 2 then control options, and 3 and 6 are up and down. BE AWARE THAT USING THE AGING SETTING WILL DAMAGE YOUR CRT. Be sure to record the settings you start at.

When you're done you'll need to save your settings:

Mute
12

That will save your settings. You can then power off the TV and power it back on.