The Dynamic Rules look at courses as a whole so it can automate actions based on various course completion statuses, so it won't include options at the individual activity completion level. Consider these options:
T
he Pulse plugin (https://moodle.org/plugins/mod_pulse) -- it's capable to send reminders for after specific dates if an activity remains overdue. Since Relative Dates is considered an experimental feature at this time, I do not know if it knows to utilize the student's relative due date or not, but if you create a test course with relative dates enabled and pick an activity with an upcoming due date, then set up this plugin in the course to send an overdue message, you can then enroll a a test user after that due date has passed to see if they will get the message on their respective due date.
Upcoming activities:
Both the plugins mentioned above state they have capabilities to send notifications about upcoming activities.
Then, there's the built-in Moodle's Analytics system's
model for Upcoming activities due (if it's not there by default, you just click add a New model). This will send emails or Web alerts (depending on how the site admin sets up default Messaging - Notification Preferences for "Insights generated by prediction models") at one of three defined intervals: Upcoming week, upcoming 3 days, or upcoming fortnight. With that said, it wont provide a list of the activities, instead it directs users to the
dashboard's timeline where they can see/access the upcoming activities. To give it a try with a test user, it's rather simple to set up and get going - while you are testing this out you can turn off these notifications at the site level, then edit the preferences of your test users and enable it just for them so only get that email/web alert. Another option to see the data it will generate for the test users is to go the Analytics Models admin settings page, find the upcoming activities due model and select the test users from the dropdown in the Insights column (they will only appear here once the analytic model has finished running for the interval) to see if they have any upcoming items due data generated, or next to that dropdown select "Actions - Insight Report" and then the particular user to see a report of the data.
These are the approaches that I have used in my institution so just wanted to share in case you see any value in these options.