While I love cool toys then alcohol works fine for finding shorts but if you have it then why not, can also be used to find open circuit in some cases.
Anyway power supply wise. If it is a good one/basic requirements for repair work one it will have a current limiter and voltage limiter option on all its channels. Learn to use these.
You might also have a voltage preset for turn on -- if you were playing with 24V for something you don't want to be sticking that down something more used to 1.8V. Bit annoying to set it upwards every time but not as annoying as toasted device (I would say ask me how I know but frankly ask anybody that has been in the repair game for any length of time).
If you know the caps are shorted already then why are you injecting power into them? Only thing you would want to be doing that with is ESR testing (equivalent series resistance, you shove a high frequency voltage into them and measure the resistance, usually another device to buy as I doubt you will have one on a meter and I would be stunned if that supply is going to be up to much on that front either).
Have not seen any schematics for this sort of purpose (mostly just known failures). However working switch to pull examples from is probably a good start there. Can also use that to bell out with a multimeter in resistance/continuity mode, and maybe an oscillscope with capture features to figure out initialisation routines*. In an ideal world we would also have Switch equivalents of
https://circuit-board.de/forum/index.php/Thread/13913-STRIP-CLUB-PCB-Scans/?pageNo=1
Edit. Apparently we do have nice sanded PCB shots of all the layers. See post below this.
I am also not so sure how useful an external power source would be -- it is occasionally done to inject power into devices to maybe power up a sub system if part of the supply/initialisation failed so as to check for failures there**. On rare occasion you might pump up the voltage to cause that little bit more heat to appear more quickly, or stabilise something that is running on the edge normally.
*some things will only turn on after another line gets a certain signal, or a signal for a given amount of time. This sort of thing you will be wanting an oscilloscope for, and knowing how to use that. Indeed I would have probably picked one up in preference to the thermal camera.
**if say a power supply goes pop then sometimes said supply will go out with a massive voltage spike. Said spike might kill things downwind of it so you might want to know if the rest of the device is working before you go to the hassle of replacing the supply. Your supply then producing all the various things the original would have before it went (you may also want to isolate what remains of the original supply in this scenario) with which to test the next part of the device.
Youtube wise... not really sure what to link for more basic stuff here in a condensed form. People playing here often have all the schematics, they know enough about electronics design, or maybe spent ages with a working device and looking up parts that they can hone in on things.
and a good chunk of the rest of the channel does good things here. He will be more on the master electrical engineer knowing enough design to figure out what is going on side of things.
He normally does teardowns of devices but understanding how they work will do wonders here.
Those two will probably also have guides to benchtop power supplies.
Many would point you at
https://www.youtube.com/user/rossmanngroup/videos
He is very good at what he does (which is repair of things), however he also usually works with schematics which you don't have in this scenario and thus I am not sure how useful it will be for you.
is more analogue radio/audio side of things but he is good at that.
I like this channel a lot, and have learned much from it but whether it is that useful here I don't know.
https://www.youtube.com/user/julius256/videos http://www.youtube.com/user/mikeselectricstuff https://www.youtube.com/user/jjward/videos
If you can't learn things from those guys you are going to be troubled (wonderful channels one and all), how useful they will be here I don't know though***.
***if you are asking for a schematic rather than asking for one in favour of belling it out yourself and measuring voltages in normal operation/startup yourself then you are somewhat behind the position that might be nice to make a real start in this arena. Not impossibly so by any means but enough that I note it.
Though if you want
Take a picture of the PCB, both sides.
With varying colours take your continuity probe and measure on a working board the continuity between various pads and other areas. Resistance too if you want, also be prepared to answer why some things in circuit might be different to what you get when you desolder them (or one leg of them).
Voltages compared to ground in various locations when off, when off but charging, when on, when on with power lead in, if screen needs to be disconnected then that too and if you are exceptionally bored then when docked as well (very much an optional step but some might tweak a dock rather than using said external supply). If you want to take the earlier stuff and the voltages here and figure out rails in this setup then that would be good.
Repeat said voltage measurements with your oscilloscope when changing between states.
If you want to take a picture with your thermal camera of a working board in the various states covered above then do that. Try to get it so you can overlay the board pictures you took at the start, though no great loss if it is too tricky as these will mostly be for spot the difference purposes anyway.
Somewhere in all this you will have wanted to look up the schematics for whatever chips have numbers on the top. Hopefully Nintendo/Nvidia has not used too many out and out custom chips for this one. Do note many such things come with reference circuits so the passives surrounding them might be detailed too.
From here we start getting into reverse engineering and failure analysis design type approaches -- heat, bad voltage regulation and high voltages in general, especially if at or exceeding the general limit, is what kills electronics. What do you see that is running hot, or operating near/at/over what the manufacturer suggests. Do you see any fuses or things acting as them (ferrite beads, 0 resistance links...)? Mechanical failure is another thing; most prominent will be people ripping sockets off the thing (ever had a phone/laptop/tablet with a charger port you have to keep at the right angle? This is likely that). Part of design will also likely see you know what the standard resistor series values might look like which could help with that in circuit, not in circuit thing above.
You can also look to see what known failure modes there are (I see many around here, starting in the earliest days when people were shoving unblessed USB-C cables into the thing and finding Nintendo maybe did not anticipate that one).
