I confirm that there is no battery backup, which is fully understandable given that the B710 and Studer A710 were never intended to be alarm clocks - which is also why they do not display the time when they are off. Programmed recording/playing is not their strong point, but if you look at the history of their inception they were designed to be high quality recorders/players with studio operation in mind, and were the best that the technology of the late '70s could offer in this domain. Real-time clocks, OTOH, did not come for free at that time, and consumer-oriented functions such as programmed recording were clearly not part of the basic requirements, it came as an afterthought.
In fact you need to know that, just to keep the real-time clock running while the B710 is "off", the latter is not really turned off. It is just in a different mode in which the capstan motors are not running and the display just shows a dot, but the CPU board is still fully powered (the clock is actually derived from the CPU's clock by a piece of software) so the deck still draws non-negligible power when turned off. This is not sloppy design by Studer, just how things were done with the technology available at that time, but that means that you are probably better off powering it from a switched socket than trying to display the clock all the time. That clock is not terribly accurate anyway, since it comes from an ordinary 4MHz crystal instead of a watchmaking-grade oscillator. One cannot expect 40-odd years old equipment to have all the refinements of 2022 equipment.
Sorry, I know that this is a very popular internet myth, but as an engineer I have to lecture you in 1980-ish electronics, and sorry if I sound harsh, this is not my intention. These parts were not cheap or horrible at all. On the contrary Revox used some of the best parts available at their time, including the tantalum caps that "internet experts" despise today. These capacitors were actually 5 times more expensive than their chemical equivalents, and were chosen because they were better (that is, than the chemicals of their time), and they were perfectly suitable at the places where their were used (ie. never reverse-polarised). The engineers who designed these machines were definitely neither bozos nor cheapskates, but they had no way to know (a) that some people would still use their products 40+ years later, and (b) how long components would last. Seriously, Studer used mostly the same parts for their broadcast and studio equipment (the main exception is the trimpots, which were usually industrial types instead of Ruwidos), and it's not just Studer. For example I've just restored a bunch of Schlumberger recorders that were made roughly in the same era, designed without compromise for trouble-free 24/7/365 operation in nationwide radios, and I for one was not at all shocked to have to change many electrolytic capacitors and ball bearings (let alone the pinch rollers and heads), clean most switches and pots, and recalibrate everything. The Nagras are (usually) less trouble after all these years but, in order to achieve that, they were made with aerospace-grade components and cost the price of a decent car. This is just normal aging, if you cannot accept it then vintage equipment is probably not for you.
Getting back to your problem: after reading your posts, I am not sure if you did more than change the electrolytic and tantalum caps and the spooling motors. If not, then you did not really restore your B710 so problems are definitely possible. You really need to change the trimpots as well (much more troublesome than the caps: I had to change almost them all, on all the Revoxes I've had in my hands, as the wipers have gotten brittle and break by just looking at them), plus the usual cleaning and lubrication of the transport with PDP65, and then follow the service manual to check and calibrate everything. It wil take time, skills and equipment, and I wish there was a cheap way to make a 40-years old deck (any deck, not just a Revox) work as it should. Unfortunately, experience and training have taught me otherwise. The good news is that, if you cannot do it yourself, there are a number of professionals out there who can do it for you, including Revox service centres (yes, they still exist!). The other good news is that, once properly restored, your B710 is a great deck, well worth the effort.
There is more to a power supply than a cap. I have seen power supplies that had the correct voltage when unloaded, but collapsed once they had to provide current, due to a faulty rectifier for instance. You do need to measure (with the proper instruments), assuming is not enough