aww, the poor love
not nice, but at least he has a relatively short coat, so it won't stick to his bum feathers like it does with our lad
as it's usually an "i've eaten something i shouldn't have" situation with him, where he's still quite happy and generally "himself" but just having trouble in the poop department.
we usually feed his normal basic kibble diet for the first day (no treats), if it doesn't clear up with normal feeding, the next day he gets two doses of kaolin (one on a morning, one on an evening) and gets a couple of rich tea biscuits instead of his kibble meals, just to line his stomach. (this instead of the 24hour starvation, as this has led to him sicking up bile, due to having an empty stomach in the past)
within 2 days he's usually back to his "regular" self. or at least firming up. if it's the latter, we continue with the kaolin for another day and re-introduce his kibble, giving him small meals and working back up to normal portion sizes.
we went through this a lot when he was younger as he had a teenage phase where the slightest different thing would set him off and it would fly out of both ends (immediately) then just the back end for a few more days.
much rarer these days, usually just the bottom end nowadays too, but we always keep a packet of biscuits and a bottle of kaolin in "just in case" the last lot got thrown out due to expiring, so we've just bought a new lot.
we found this to be the best way to firm him up, but every dog is different.
the chicken and rice diet is what is usually recommended and does work. (the dog usually loves it too)
our old dog used to just pick the chicken off and leave the rice though! Bless her.
I've also heard of poached fish and potato, or scrambled eggs settling an upset stomach as well, but neither of these have suited my boy, he's not an egg dog at all and fish makes the situation worse.
if it goes on for more than a few days though, or he doesn't seem to be drinking, get in touch with your vet again OP, or if your dog isn't quite himself at any point, make a phone call to get him checked over
don;t worry too much though if it's just a runny bum, this weather is causing all kinds of troubles for everyone
all the best x