Pretty boards----very "Philipsy"!
Yes,the 3 pin caps are for better physical stability---if I remember correctly,Sony used them, too.
The round glass encapsulation on the diodes was fairly common,back in the day,--nothing special about it.
The diodes in the rectifier in the switchmode output circuit do need to be fast-recovery types,but the ones which rectify the mains to give around 300 volts DC don't.
As the thing is "squawking",it seems like it is getting mains power,etc.
There may be excessive load on the supply,so it may be an idea to remove some of the loads to see what happens.
As this is a Philips circuit,it may need some load to operate (some switchmodes don't,some do),but it should be OK it you remove them one by one---be very carefull--this board has 240v AC,probably 300v DC,& DC 2100v on it !
The only circuitry which handle significant power are the deflection circuits,so if you disconnect them first,the supply may come back up.
Anyhow,have fun,but,again ,Be Carefull!
I have seen quite a few of this generation of Philips 'scopes on EBay,mostly at bargain prices,but I can't remember seeing any in service anywhere I worked.
There were usually a few of much older vintage,& lots of Philips LCR bridges,Signal Generators & the like.
I wonder who bought all those PM3055s originally!
VK6ZGO