Well they are good for a couple of months, I wouldnt over do it.Make sure you are storing in TE rather than in something like RE buffer , for two reasons. Pure water absorbs CO2 from the air and becomes acidic, which trashes DNA. And small amounts of contamination from fingers, e.g. will add magnesium, which acts as a co-factor to many nucleases. TE buffers at pH 7.5, and has EDTA to chelate the magnesium
It really depends what you intend to do with it. If you just wish to run it on a gel and analyze it, then it is probably good for some time. If you want to clone fragments, then I would use it sooner rather than later. If you replace the RE buffer with TE, that will help stabilize the DNA but of course the EcoRV enzyme won't be able to digest your DNA.
After DNA digestion, I will dilute the DNA digest followed by assemble PCR reaction then the sample will be pipetted into a cartridge for droplet generation. I will perform ddPCR.
dsDNA itself is quite tough. PCR products can be left at RT for probably a week. However if possible I would always store my DNA in Tris 8.0 10mM. EDTA is just not convenient with many other processes and stability-wise, if you're storing in -20 in the first place, EDTA probably wouldn't help much.
Now if your goal is to do PCR, why would you have to digest it in the first place? If you just want to run a restriction digest gel AND do a ddPCR, do aliquot your initial template and separate your reactions. If you actually need the digested product as template for PCR, I recommend you at least do a kit cleanup (gel purification or simple PCR purification kit would suffice) on the digested product before you PCR that.