Look at the time of the last modified file when checking out

Currently, the check out uses the time when you run `amser out`. But it would make more sense to do it based on file modification time. For example - if you forget to end a session overnight.

Start by locating the implementation of `amser out` and checking how it currently chooses the checkout time. Done means checkout uses the last modified file time rather than command invocation time, including when a session remains open overnight.

Written by the indexing model from the issue text.