I have experimented with many different hobbyist boards over the years and none of them were what I would call accurate time keepers unless they had an external RTC.
Espruino is a JavaScript interpreter for low-power Microcontrollers. This site is both a support community for Espruino and a place to share what you are working on.
No, DS3231 will definitely be better.
However the Pico should be accurate enough for a lot of things. I'd be hopeful it'll be off by significantly less than 1 second a day.