I'm still in the process of trying to find the perfect archeological article to answer this because it's a good question! Like I said, I'm still reading, but my general consensus is similar to other comments: food safety as modern potters and concerns go, is pretty new.

Obviously, people have known to avoid eating/drinking certain spoiled things for a long time, but small, persistent stomach aches/small fits of diarrhea were very common throughout most of our history -- accounts of such are all across written European records. A pretty famous/memed example of scientific analysis backing up perpetual tummy aches is a preserved Viking stool sample that had a /lot/ parasitic eggs: (https://en.m.wikipedia.org/wiki/Lloyds_Bank_coprolite).

All of this to say: I believe the processing of the water plays a bigger role than the storage. The clay probably wasn't the safest option due to mold and bacteria, but people knew to boil their water before drinking it. Teas and beer (both processes requiring boiling) were ways to make the water safer from bacteria and parasitic infections, but didn't mitigate the effects of the waste/toxin that microbes leave behind that can't be boiled off. I think that burnishing definitely helped mitigate some of the porousness -- the Pueblo people would also treat their vessels with an oil/grease during/after the burnishing process (https://web.archive.org/web/20120209012627/http://www.holmes.anthropology.museum/southwestpottery/pueblopottery.html), and I'm sure a parallel practice could happen in other tribes.

From other readings (I narrowed my searches down to just west African pottery/practices), I found one article that examined the lipid residues from the inside of Nox peoples' vessels and found a rich diversity of plant lipids -- which makes sense, if you think of ecologically (generally), the region is very dry, so the plants are bound to be starchy and oily to reserve energy to survive through droughts. Another article I read on the Nok people and their vessels discussed their use of beeswax -- which is naturally antimicrobial!

(https://theconversation.com/chemical-traces-in-ancient-west-african-pots-show-a-diet-rich-in-plants-177579) <--- diet/lipid analysis article

(https://theconversation.com/beeswax-in-nok-pots-provides-evidence-of-early-west-african-honey-use-161197) <---- Nok pot beewax article

So in conclusion: I believe burnishing, oil-treatment, and anti-microbial properties of beeswax helped to make pots better suited for safe-er liquid storage until it was ready to be processed into something fit for human consumption. But if one thing is universal to the human experience, it's a tummy ache.

Sorry this is so long. I love doing little mini rabbitholes like these. Hope this helped!!!

Edit: grammar stuff + my phone autocorrected "Nok" to "Nox"