Your Ch2 appears to be working, so the problem has to be something specific to Ch1 and not in common to both channels. For that reason, it would not be the HV or CRT adjustments. And it would be best not to mess with any adjustments until you figure out the Ch1 issue.
Offhand, it looks like something might not be making contact. It could be a relay in the attenuator, or perhaps a bad contact on the Ch1 preamp socket.
Do you have another scope for troubleshooting? If not, since your Ch2 appears to be working, you can use it to probe around in Ch1.
To start, I would suggest connecting the square wave signal to Ch1 and look at the Ch1 attenuator output, labeled "B" on the schematic. You'll need to take off the small shield to access that area. See if the output has the same shape as what you're seeing on the screen. And use a 10x 10Mohm probe since the impedance is high at that test point.
If the waveform has the same curved shape, the problem is in the attenuator. If not, look further downstream in the signal chain.
You could try reseating the Ch1 preamp, and/or looking at its output to see if the problem starts in the preamp.
You may also find the test setups, test points, and waveforms in the schematics to be useful for this problem.
If you have another scope, an easy to way pinpoint the problem is to feed the same square wave to both Ch1 and Ch2 and then start comparing the same test points in each of the channels. Find out where the waveform starts being different between the two.