Issue Running Commands on Amazon Linux 2023 t3.small EC2 Instance

Hello.

It may depend on the command you executed, but does the answer at the URL below solve the problem?
https://lists.fedoraproject.org/archives/list/users@lists.fedoraproject.org/thread/XQLTADPT4TLNCL2GZUAOLMBEACOGOKYP/

Check for lock files.
ls /var/cache/dnf/*pid
If you have any remove them and try running dnf again.

when I attempt to run any command, I encounter the message "Waiting for process with pid to finish,"

Any command? So if you run date or whoami or echo Hello you get this error?

As @Riku_Kobayashi also identified in his answer, the error message is consistent with dnf (or yum in the old days) trying to be run while there's a dnf/yum process already running. But it can also happen if a previous dnf/yum process doesn't exit cleanly and leaves a lock file.

In your three-stage solution that you outline, when you have a t2.small and installed every thing on it do you do a dnf update -y as part of step 1? This would mean the RPMs are already at their latest versions, so in step 3 when you deply the new AMI on the t3.small, a dnf update -y will complete more-or-less immediately because there's nothing to do. And once dnf has completed you will not get Waiting for process with pid 12345 to finish.