I sense a frowned brow about why the speed of the output transistor should be a factor when you "just want a steady 10Vdc output.
Loop stability is a serious concern with any control loop.
And loop is the magic word here.
Loop implies feedback.
To stay with your example: A steady 10Vdc output.
In your schematic one of the two uA723 voltage regulators measures the output voltage with a voltage divider, and compares it with it's internal voltage reference.
If it sees a too low output voltage, then it opens up the output transistors more, if it sees a too high voltage, then it closes the output transistors a bit.
There always is noise in the circuit, and the uA723, together with the whole output stage adds a lot of amplification (T2, T3 & T4 through T8).
So assume the noise makes a peak, and the uA723 measures 10.005V instead of 10.000V.
In that case it tries to lower the output voltage to get back to the set voltage, but it takes a bit of time (micro seconds, or some tens or hundredths of nano secons) to do so.
If the control loop is maladjusted, then at the time that the output voltage reaches 10.000V, the uA723 has actually over corrected because of the the time delay of it's output signal through the output transistors, and even though it "stops lowering it's output voltage", the output voltage may shoot through a bit and go as low as 9.992V. So then a bit later, the uA723 notices the output voltage is now too low, (8mV, while it first was 5mV too high), and it will increase the drive level to the output transistors. And in this maladjusted example, it then will drive the output to 10.012V, en then to 9.985V, and this escalates until the whole power supply is a big oscillator.
The speed with wich this occurs is partly defined by the semiconductors, (uA723 itself, output transistors) and partly by (Usually) capacitors added to the circuit, which form RC constants.
Your power supply has the output capacitors (C4 & C9) as most power supplies do, and this lowers the speed with which the output can change voltage.
There also is C1. Which is connected to the raw output of the bridge rectifier on one side, and the parallel combination of R7 and R22 on the other side.
C1 = 150pF
R7 = 4k7
R22 = 22k
So these two resistors are 3k87 in parallel, and with the 150pF capacitor it forms a time constant of
3k87 *150pF = 580ns which resembles a frequency of around 270kHz.
So that would be the maximum speed at which the the output reacts to the voltage differences dictated by the uA723.
I may have some gross mistake here, It's been years since I last did this.
The whole thing is much more complex, because it involves the speeds of each and every component used, and even wire length and PCB routing can throw it off.
A quick search:
https://html.duckduckgo.com/html?q=power+supply+loop+stability... shows up much more in depth information.
Here a method to measure the actual delays in a power supply circuit:
https://www.omicron-lab.com/fileadmin/assets/Training_and_Events/Webinar/2014-11_Webinar_LoopGain.pdfAnd this search:
https://html.duckduckgo.com/html?q=home+built+injection+transformerbrings up:
https://adilmalikn.wordpress.com/2019/07/07/homemade-inject-transformer-for-psu-loop-analysis/