Welcome @matthew1201 
!
Of the Labs solutions out there the Envelope Budget is the only one that allows for weekly budgeting periods. It’s a really powerful solution, but it’s not getting any dev attention right now nor will it likely in the future. We released the Savings Budget as a more performant alternative for “rollover” budgeting, but that one doesn’t offer a weekly period option.
In the Envelope Budget there is a feature that allows you to assign the Rollover To amount to a different category. E.g. left over groceries budget should rollover to vacation fund. These can be unique per budget period and all that configuration is stored in the hidden Budgets History sheet.
There isn’t an automated way to have it change the “rollover to” based on a trigger like you describe and the way it works isn’t intuitive for the way you’re used to budgeting "most of my expenses are goals" so there isn’t a concept of “it’s funded” really - money that isn’t spent is rolled over to the specified category so if you’re saving up for something (to fund it) the actual would be $0 in most recommended workflows with that budget and thus the money would rollover and be “saved.”
If you can figure out the mental gymnastics 
of a workflow that would make sense, you could probably record a macro to get you started on a script that would look for a specific value and if it’s X then change the rollover to for the specific period to a different category.
The macro reference link above is from @benlcollins website and he’s a guru for all things Google Sheets so if you have some basic programming knowledge, you can probably pick up a lot quickly from his site and this community 