Depends on whether you're hunting in the Glimwood Tangle or the Old Cemetary. Either way, authentic Sinistea has a 1% spawn rate out of everything overall, but the rate of forged Sinistea varies, meaning that your ratio of forged/authentic changes.
In Glimwood Tangle, the chance of finding any Sinistea is 11%; 10 for forged, 1 for authentic. Ignoring phases from other Pokemon, this gives you a 1/11 or 9.09% chance of getting an authentic Sinistea.
The Old Cemetary varies, both for overworld spawns and random encounters. In every weather except Sandstorm, authentic Sinistea has a 1% chance overall, while forged Sinistea has a 19-20% rate via overworld spawns and a 13-19% rate via random encounters. Here are all the rates:
Sinistea cannot be found during a sandstorm.
Clear weather, random encounter: 19:1 ratio; 1/20 or 5% chance
Thunderstorm, random encounter: 13:1 ratio; 1/14 or 7.14% chance
All other weather (except sandstorm), random encounter: 17:1 ratio; 1/18 or 5.55% chance
Blizzard or fog, overworld: 20:1 ratio; 1/21 or 4.76% chance
All other weather (except sandstorm), overworld: 19:1 ratio; 1/20 or 5% chance