I'm quite interested in this topic and had tentatively reached the conclusion from digesting hundreds of websites that moving away from a switchmode supply was a no-brainer for all the digital signal devices in my hifi.
Sad to say, though, when I recently connected my raspberry pi (with DigiPro hat) and its wired harddrive (self-powered) to two separate power packs I could not (definitively at least) hear any difference. This was an initial test to find out whether it was worth buying 3 linear power supplies (including another one for my DAC).
Now, these lithium devices have quite high internal resistance (apparently) compared with, say, a nickelhydride battery or 'supercapacitors" so my result isn't conclusive. Also, my SMPS devices always run off a power conditioner that reconstructs a sine wave at tightly defined voltage (overkill but is the result of previously blowing a preamp), so 'mains' noise was never an issue for me (though I thought the whole point of the exercise was to remove noise created by the SMPS devices themselves).
Of course my sound system may not be sufficiently resolving (fairly likely) or my abused 50year old ears may not be up to the job (very likely). Anyway, while I'm always looking for the next item to buy, at this stage I'm leaning to the idea that SMPS devices have become adequately quiet for my purposes - indeed some websites claim to have recently tested off-the-shelf SMPS adaptors and found essentially zero noise.
Bottom line is I will look to upgrade my DAC or speakers before worrying about power supplies.
Might I just toss in that the Rune audio software is fantastic and I am so appreciative and in awe that the Rune team put together an image for the DigiPro so quickly.