Just tried to “buy” a gift card >2,000: would not allow (see attached). So seems like 2,000 is a hard (undocumented) limit for the account.
Apple Gift Card(s) – up to eight + Apple Account balance
You can use up to eight Apple Gift Cards at a time when you purchase online from Apple or if you’re placing an order by calling 0800 048 0408. You can use your gift card(s) with an Apple Account balance and Apple Pay or one credit card.
You can use up to eight Apple Gift Cards for one transaction when you purchase at an Apple Store.
So can put up to 2k in the account and use the remaining card(s) for the rest of the payment. In theory, looking at possibly doing 18k in balance plus 2k valued gift cards.
In the 2.5k case, Apple Store employee would need to issue 10x 250 valued cards to mess up the number of cards restriction (just get 2x 1k + 500 or 5x 500 cards)
But, yeah, bad suggestion by the store employee to add to the Apple account if intent on buying in person.
Would be interesting to see where you saw “there’s no way to use the remaining physical gift card balance to complete the purchase online”. Does not make sense as Apple knows what the remaining value of the card is, so should work similar to a full-value card (ie. look up value, deduct from purchase, new net purchase cost to go on some other payment method when online or via toll-free call).
Personally, I always order whatever I want to buy via the Apple Store app/website and then go to the store (or ship to home if pre-ordering a new device), so no issue with the limits imposed and not wasting time making the drive to the store and find out not in stock.