Hi,

Due to official docs on How to install MongoDB on Ubuntu:

Important

The mongodb package provided by Ubuntu is not maintained by MongoDB Inc. 
and conflicts with the official mongodb-org package. If you have already installed
the mongodb package on your Ubuntu system, you must first uninstall the mongodb 
package before proceeding with these instructions.

https://docs.mongodb.com/manual/tutorial/install-mongodb-on-ubuntu/

It seems to be easy when you do not have any database deployed with MongoDB 3.x and you want to just start from scratch. You would uninstall version 3.x, and install 4.4.
But you asked about updating (upgrading ?) from version 3.6.3 to 4.4, so it looks like you have the database already deployed. I am going to quote official doc again :)

To upgrade from a version earlier than the 4.0-series, you must successively 
upgrade major releases until you have upgraded to 4.0-series. For example, 
if you are running a 3.6-series, you must upgrade first to 4.0 before you can 
upgrade to 4.2.

When you have your MongoDB upgraded to 4.2, then you will be able to upgrade to 4.4.

So, what I would do:

1. Create a snapshot of your droplet, to be able to restore the current, well-working environment, in case of failure.

2. Create a new Ubuntu 18.04 droplet, and install mongodb-org ver. 3.6.2. You can download it from the official site:
https://www.mongodb.com/try/download/community

3. Transfer the database to your new droplet.

4. On your new droplet successively upgrade MongoDB to version 4.4, due to official docs:
https://docs.mongodb.com/manual/release-notes/4.0-upgrade-standalone/
https://docs.mongodb.com/manual/release-notes/4.2-upgrade-standalone/
https://docs.mongodb.com/manual/release-notes/4.4-upgrade-standalone/

5. On your old droplet uninstall MongoDB ver 3.6.3, and install version 4.4, due to this doc:
https://docs.mongodb.com/manual/tutorial/install-mongodb-on-ubuntu/

6. Transfer your database from the new droplet to the old one.