Cannot change shell to zsh

After upgrading to macOS 10.15, I got an alert in Terminal that the default shell is now zsh, and to run `chsh -s /bin/zsh`. This, however, gives the message: "chsh: no changes made".

So I checked a number of things:

• "echo $0" returns "-bash", indicating that I'm still running bash.
• I double-checked this by looking at the process chain via "ps -al".
• However, "echo $SHELL" returns "/bin/zsh" – liar, liar, pants on fire!

Based on Apple's support article and various other posts, I unsuccessfully tried a number of fixes:

• Set the default shell via the Advanced options in Users & Groups, as described in the Apple article.
• Set to use the default shell in the Terminal Preferences, as described in the Apple article.
• Set the Terminal preferences to explicitly use /bin/zsh.
• Since I am joined to a Microsoft Active Directory, I tried changing the shell in the Active Directory, as described in this Apple support article. However, the account I'm using is actually a local account, as verified by "dscl /Search -read /Users/"$USER" | grep AppleMetaNodeLocation", which returns "/Local/Default", so it's not surprising that this did nothing.
• I know that I could start zsh from my bash profile, but that's just plain ugly.

Anyone have any suggestions?