Is the 100% featured character chance carried over in the new banner in Genshin Impact?

Yes, the pity status is carried to the next limited character banner. So, in this case, you are bound to get the Geo Archeon because of the 100% limited character pity since your previous one was a standard pool one.

For reference, take the text in Venti banner

For Event Wish "Ballad in Goblets": Base probability of winning 5-star character = 0.600%; consolidated probability (incl. guarantee) = 1.600%; guaranteed to win 5-star character at least once per 90 attempts. The first time you win a 5-star item in this event wish, there is a 50% chance it will be the promotional character "Windborne Bard" Venti (Anemo). If the first 5-star character you win in this event wish is not the promotional character, then the next 5-star character you win is guaranteed to be the promotional character.

The description is indeed unclear but the meaning is that banners of the same class - so Limited/Weapon/Standard - share the same pity counter. So, if for example you are on 50/90 when Venti banner ends, the pity counter for the Limited character banner will still be 50/90 on the next one. The 50/50 vs guaranteed pity class carries over to.

Now the real question is... Zhongli or Lady End User License Agreement?