> it does not mean the bank would charge me interest on my savings (which would of course cause me to withdraw my money and close my account).

Indeed. The reason why this matters, and becomes possible, with a CBDC is that there is nowhere left to "withdraw" to. Private banks would not offer you any higher rates on savings than the CBDC does (why would they, when they can borrow at the interbank rate for less?). The fact that account holders would withdraw if rates on savings became negative is why central banks presently are unable to reduce the interest rate (significantly) below zero. With a CBDC, "withdrawing" simply means transferring from your private bank account to your CBDC account.

It would not be the government enacting this policy, but the central bank itself, as a necessary step to conducting monetary policy below the zero bound.