Great questions. While I understand the rationale for your creating a second savings account, that option is more complex than I would have chosen, especially if it is short-term savings. If it were long-term savings, your approach provides some advantages, since you could place the funds in a higher-yield, interest bearing account and earn some money while the balance builds.
(Ideally, your Emergency Savings should be longer-term, and your moving funds there for the future can help you both sequester the funds from other uses and deposit them in a higher-yield, interest-bearing account, with little or no penalty for early withdrawal, while you wait (hopefully for a long time) for a true emergency.)
But for the shorter-term expenses such as technology, gifts, vacations, etc., my approach is to budget monthly for these and let the available funds build in my source account (Checking) over time, and visibly assigned to one of these categories in my budget.
So with this approach, I would simply assign purchases toward those short-term items to their appropriate category, as availability allows (the Available column of the Savings Budget.)
The beauty of the Savings Budget shows up, though, where you may redistribute savings from other categories to a particular need. For example, if you have been saving for a vacation, and decide to take it sooner than you thought and your budget for vacations is short, you might find the funds to cover the difference you need by moving savings from another category in the Savings Budget sheet to Vacations.
The tool also allows you to access savings in a category from previous years and reassign it, as well. The time frame for this availability matches the time frame of your Categories sheet…(multi-year). So you could save for a vacation over two years by letting the funds in your Vacation category build up, unspent, in your checking or source account over time.
Does that help bring these ideas together? Apologies ahead of time if I have added to rather than reduced any confusion.