In the azide process a Tungsten (or possibly nickel) filament was first oxidised, or a copper layer on the filament was oxidised. The anode would be initially coated with barium azide. In manufacture, during vacuum pumping, the anode would be heated to vapourize the azide. At high temperature the vapour would decompose to form barium and nitrogen. The barium would react with the oxide on the filament to form a barium oxide layer on the Tungsten. The barium also deposited itself on the inner surface of the envelope where it acted as a getter to absorb the final gas molecules after the valve was sealed. One conspicuous feature of the Mullard form of the azide process was heavy internal blackening of the glass bulb (eg PM22). This was OK while competitors’ valves were equally black (although some used a magnesium pre-getter to make the glass look silvery rather than black)
Later when Mullard & Philips adopted the the paste coated cathode which replaced the azide process they continued to use the “red” coating, even on valves which didn’t require external coating as a kind of “trademark”. Gold colouring was also used.
See also the Radiomuseum articles by Jacob Roschy
The second reason is an electrostatic or RF screen using conductive paint. Actually if the paint is loaded with Nickel it also adds magnetic screening. Later valves use an internal solid, perforated or mesh cylinder around the electrodes (mostly anode) which people may mistake for an anode. RF types may use an open mesh as a compromise between screening and capacitance as the internal screen increases the capacitance from Anode to ground or cathode. On RF types it may be connected to g3 or equivalent rather than cathode.