When you replaced the seats on the hot water valve, did you depressurise your entire system? For how long was it depressurised? Would you in any way, intentionaly or accidently hit/smacked/braced against/on the cold water valve or pipes imediatley around the tub's cold water valve? 35+ years.... first owner? Original plumbing? Are the pipes steel (and @ 35yo

I found your problem most likely), or what are they?
You're sure it's only the cold water faucet in our house with this problem though? Since it's a good and cheap thing to do anyways, will probabley get some good answers if any are to be had, and I just know you love to play plumber - I recommend you do the valve seat on the cold water faucet/valve in the tub too. Pay attention while dissasmbling for any corrosion or debri clearly visible. BEFORE reasembling the valve, but after you've removed the old seats, we're gonna want to flush out that cold water pipe. Try to do two... well three things when you briefly flush it out by turnign the water briefly on then back off. Avoid water hammering your system by turning the water on too fast at the main valve, while also being brief and fast and gettign a good flush through. Second, avoid making a mess or hurting anything/one which ties into the third thing - try to strain/catch the flush in a rag or sponge, this will minimise spraying water 20-ft across your bathroom while also revealing/catching hopefuly some evidience of what is hopefuly debri/crud. And do be careful - at best it's an old chunk of lead solder from your old pipes and the aprentice plumber that helped install them - and it will come out of your pipes in the flush like a shot (I got a funy story about that, I was on a ridealong with the fire dept to shutoff a sheared hydrant one day, two guys holding up a tarp to shield the shower from the one cranking the street valve, and one of the tarp guys suddenly falls to the ground like he took a ~10lb sledge thrown 50-ft up to the top of his head - he did, chunk of dislodged over-generously-aplied lead solder).
I'm not a plumber, but I design and engineer commercial irrigation systems to pay the bills.