The day 1 update removed 10 base hp from Ting-Lu's stats so I'm wondering if it got down to 1 HP on version 1.0.0 and then the game updated it to version 1.1.0, would Ting-Lu still have 1 HP or would it be glitched?
No.
Scarlet and Violet may be a buggy mess, but this is one problem they don't have. A Pokemon's HP at any given time is a percentage of its total; rounding dictates Ting-Lu will not drop past 1 HP, even when its maximum is decreased.