"In response to terrible interest rates from banks, it seems they're just sitting on piles of deposits from their customers - obviously saved up over the past couple of years being locked up at home. So essentially they don't need to offer increased interest rates to savers as they have a large base from which the lend money out."
While it seems that this is the logical way that banks should work, they actually don't.
They don't typically lend money from their reserves. In fact their reserves represent only a small fraction of what their books actually account for.
The way the fractional reserve banking system works is that when they lend, it's brand new money, created at the click of a button - set up as debt from the get-go.
When the Reserve Bank floods the market with new money, the banks get it in the form of credit to lend out, hence why no matter the economic situation, the banks are always killing it. It's called the Cantillon Effect I believe.