Regarding your first question:
Is there a calculation in the Budget Health columns (referenced above), which indicates how much the total Available amount in my budget is different than the total amount of funds I have in the bank?
The Budget Health calculations are more designed around a balanced (expense vs income) budget because, even if you’re “on budget”, if your expense budget is larger than your income budget, you shouldn’t accrue any rollover savings. These calculations also do nothing to compare to balances. That is part of the secret sauce of the Savings & Debt template since it allows you to connect budgeting “savings” to actual account balances.
Regarding your second question, your approach makes sense but I agree with @matt, that it may make more sense without the current-month budget included. These values are available to you in the hidden area of the Savings Budget in columns AP (including Budget Journal adjustments which @matt also makes a good point about).
And if you want the current-month budget included, you can just leverage column AQ.
It is unfortunate that the values in AP will depend on the period selection in the Savings Budget sheet. In other words, if you left an old period selected in your Savings Budget sheet, your dashboard— wherever it lives— would not render the correct numbers. I believe I rebuilt a simpler version of these calcs (for this reason) into the (hidden area of the) Savings & Debt template. You could consider copying them out to create a standalone dashboard.
Also, to @matt’s point about hidden categories, you can see that hidden categories are fully processed in column AG but then filtered out of the dashboard. So these numbers are available to you if you reference the hidden area of the Savings Budget.
Hope this helps.
Randy