The power supply will not include leads. Standard 2.5mm banana plugs or spade lugs will work with it. Since the quality of the cables you can find almost anywhere is questionable (and nearly all of them use PVC insulation, which is awful), I recommend building your own. I use Belden 8899 test lead wire and for power supplies I prefer Pomona 4555 MiniGrabbers for low current DUTs. Whatever power connectors are common on modular synths, you might want to get something compatible with that too. I use Mueller BU-16 banana plugs. Or you can just buy them premade, Pomona makes them which you can get at Mouser etc, and there are probably eBay sellers making custom ones with decent quality cable and such.
The oscilloscope will include 4 probes. They won't be HPAK quality, but perfectly usable. I wouldn't replace them, and you may find replacements aren't well matched to the 'scope's frontend anyway and might not have enough tuning range to equalize. You might want to pick up some BNC to MiniGrabber cables, buy/build some BNC to <insert common modular synth connector here>, or BNC to banana adapters; at audio frequency and low impedance you can use them as 1X probes.
The multimeter will include leads. I haven't purchased this unit (you can probably find a YouTube unboxing...) so I don't know the quality, but I'd expect them to be on the upper end of the Chinese brands (which is to say usable but not nice). Probemaster probes come highly recommended by anyone that's used them, as far as I can tell, but I haven't used them myself (they don't seem to use distribution and their shipping rates to Canada seemed exorbitant). I use Pomona 5519A. They're nicer than most Chinese leads, proper rubber sleeving and such, but on the lower end.