Well done identifying the damage.
I wouldn’t bother using an oscilloscope to read the secondary voltage of the transformer. Sledge hammer to crack a Christmas nut! I would use a multimeter (set to ac volts) with the faulty monitor disconnected from the transformer.
If you have the oscilloscope probes set to x10, you reduce the voltage that is passed to the oscilloscope by a factor of 10. So whatever voltage reading you measure on the oscilloscope, you have to multiply it by 10.
Yes, Chinese manuals are cr*p... You need to download and read a good (old) book on using an oscilloscope. You can then apply what you learn to your oscilloscope. If you are confused regarding how to effectively use the oscilloscope, then I would treat the measurements as “suspect” until you get a bit of experience under your belt. An oscilloscope is a very useful tool, but you need to know how to operate it.
I suspect that one of the diodes has gone short circuit - causing the other to fail in the process. I had exactly the same fault many years ago, but on a very BIG bridge rectifier (30A)...
If you look at the equivalent schematics for the PET 2001 you will observe that the diodes are specified as 1N5402 (3A) or 1N4002 (1A). The voltage regulator is rated at 1A. I would be inclined to use the 1N5402 devices as replacements though.
Make sure you mark the polarity of each diode before removing them. I would be inclined to remove the two faulty devices and test them out of circuit AND test the remaining two diodes to ensure they are still functional. Either that, or replace all four (4) devices at the same time.
Warning: Putting the diodes in the wrong way when they are replaced could cause further fireworks and destruction.
It is also just possible that the voltage regulator input side has gone short circuit. Possible, but a low probability.
I assume you know how to test diodes?
Dave