Bash: value too great for base when using a date as array key

It's because dailyData is being automatically created as indexed array rather than an associative array. From man bash:

An indexed array is created automatically if any variable is assigned to using the syntax name[subscript]=value. The subscript is treated as an arithmetic expression that must evaluate to a number.

The issue goes away if you explicitly declare dailyData as an associative array:

$ declare -A dailyData[2021-02-08]="$todayData"

$ declare -p dailyData
declare -A dailyData=([2021-02-08]="" )

I can't reproduce the problem with associative arrays:

#! /bin/bash
declare -A dailyData
today=2021-02-08
todayData=whatever
dailyData["$today"]="$todayData"

But, if I use normal arrays, i.e. declare -a (mind the case!) or no declaration at all, then I'm getting the error you mention. That's because the array index is interpreted as an arithmetic expression, so for 2021-02-07, it was just calculated as 2021 - 2 - 7 = 2012, but for 2021-02-08, the last number in the subtraction is invalid in octal.