What makes "~" under sudo change between different installations?

Question

I have two computers. One, Computer A, runs Ubuntu 18.04. The other, Computer B, runs Ubuntu 20.04.

On Computer A, I have a ~/.bash_aliases file

-rw-r--r--    userA    userA    /home/userA/.bash_aliases

with the following aliases:

alias sudo='sudo '
alias runtest='$HOME/bin/test_script.sh'

The ~/bin/test_script.sh file

-rwxr--r--    userA    userA    /home/userA/bin/test_script.sh

has the contents

#!/bin/bash
echo ~

When I run the alias as both userA and root, I get

$ runtest
/home/userA
$ sudo runtest
/home/userA

(which is what I want, for what it's worth).

On computer B, I'm trying to make an identical setup. The ~/.bash_aliases file

-rw-r--r--    userB    groupB    /home/userB/.bash_aliases

has the same aliases

alias sudo='sudo '
alias runtest='$HOME/bin/test_script.sh'

The script ~/bin/test_script.sh

-rwxr--r--    userB    groupB    /home/userB/bin/test_script.sh

has the exact same contents as on Computer A. On Computer B, however, running the alias as both userA and root gives different results:

$ runtest
/home/userB
$ sudo runtest
/root

Notice that when executing $ sudo runtest, ~ is interpreted as the $HOME folder of the user (userA) on Computer A, but the $HOME folder of root on Computer B. I would like it to return /home/userB, just as it does on Computer A.

Things I've checked:

• I have sourced .bash_aliases on both machines since last editing them.

• /etc/sudoers is identical on both computers, and neither has env_keep set anywhere within /etc/sudoers.d/.

• /etc/pam.conf and /etc/pam.d/sudo are identical on both computers.

• The $PATH values are identical for both users and for both roots, respectively.

For the users:

$ echo $PATH
/home/user(A|B)/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin

For root on both Computer A and Computer B:

$ sudo su
# echo $PATH
/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games

There must be something different between the two computers, but I've checked everything I know to check. What else could explain the different behavior? Did something change between 18.04 and 20.04 that would affect this?