How to determine database read/write ratio on MongoDB MMS?
There are two way.

opcounters

Build as sum of the opcounters which are write operations, build a sum of the opcounters which are read operations set them into relation. To do this reliably for a sharded cluster, you have to create a dashboard which groups the opcounters for the shards.

network in/out ratio

This is self explanatory. But please keep in mind that you have to divide the out ratio by the number of replica set members to get a rough idea. For a sharded cluster, you need this grouped by shards in a dashboard, too.

What really comes to my mind: you should actually know if you have a rather read or rather write heavy application. Your use case, your business model (if applicable), your implementation, your integration tests: all these should give you an idea.