Unfortunately, it sounds likely to be a worn out CRT, based on many years doing TV repairs back in the CRT era.
The red gun was generally the first one to go (especially on Sony Trinitrons), because the lower efficiency of the red phosphor required a higher beam current on the red gun compared to green and blue. If it hasn't worn out too badly, an adjustment of the red gun drive/bias controls might improve it.
You MIGHT be able to wring a bit more life out of it by installing a "brightener" into the CRT heater circuit. This is basically a small step-up transformer that increases the applied voltage, running the cathodes hotter than normal, and (temporarily) increasing electron emission from worn out cathodes.
https://www.suburban-electronics.com/display/SEW-123/CRT-BRIGHTENERAfter installing the brightener, you will need to adjust the RGB drive and bias controls to get a proper greyscale balance.
Another possibility is to get hold of a CRT tester/rejuvenator (used units at hamfests or on eBay sell for next to nothing these days), and give it a shot. This isn't without risk of destroying whatever remaining emission you have, so if you go this route, start with the mildest "cleaning" function, and only use the "restore" or "rejuvenate" as a last resort.
The real cure is obviously a new CRT. But NOS tubes are becoming hard to find, and all the rebuilders have shut down.