Assigning default gear for individual activities

Are they just profiles, or are they actual bikes? Analogously, track running and track shoes are logically different types.

Edges have a list of bikes to choose from you can program

“MTB” as a profile means nothing in terms of automatic gear assignment to an activity in Garmin Connect, other than applying any default gear rules set for Cycling across the board. You haven't shown or convinced me that you can specify on an Edge device that using the “MTB” profile means you're riding a Canyon Exceed CF SLX mountain bike as opposed to a Scott Voltage

As Roypw reported above, Garmin Connect does not recognise profiles set up on Edge devices (and, in fact, has no visibility or record of the Profile data table), just as Edge devices have no visibility of the Gear data table set up in the Garmin Connect service's database.

• The bike selection made on the Edge isn't communicated to Garmin Connect. If your Edge is set to "MTB" GC doesn't necessarily update the gear usage for that bike.

It doesn't matter what the Edge user names a profile. Until you can specify a bike on an Edge device in the way it has to be specified to reference a row in the Gear data table in Garmin Connect, no, you're not specifying a bike for the purposes of assigning sporting gear to an activity.

Sorry if I mistakenly assumed that you understood the issue OP brought up.

I'd like to set up Garmin Connect such that when I choose 'run' on my Fenix 3, my road running shoes are linked and when I choose 'trail run' it knows that I'll be using the trail running shoes.

• user specification of rules for automatically assigning default gear to activities upon upload allowed by Garmin Connect do not go down to that granularity; and
  
• while I don't use a Fenix 3, I doubt you can create a custom activity profile that will record and upload a record of activity type (see Step 3) Trail Running (which is in the Type table, i.e. list of recognised types, for Activities in the Garmin Connect database) as opposed to Running, irrespective of what you name the custom activity profile. (The name may have meaning to you, but cannot be assumed to be recognised by either the system or anyone else as having logical meaning.)
  

Currently I can only select 'other' when I choose an activity assigned to my trail running shoes, 'trail running' is not listed as an option under gear settings.

I have the same problem with my road and mountain bike.

yes one would think this would be built into Connect, however this POS software never ceases to amaze me as to how hard it is to use and how lacking it is in features. The most frustrating software I have used in many years, manufactures just don't put out junk like this these days

Very surprised there have been no answers to my post, guess it's not something Connect can do?

Any way to set a default 'Gear' type by activity?

No. The only type of automatic gear assignment rule you can set, to be applied by Garmin Connect upon data for an activity being uploaded to it, is by type (running, cycling, etc.) without taking into account the sub_sport (treadmill running, indoor cycling, etc.); furthermore, the facility for adding automatic gear assignment rules in Garmin Connect only allows the user to select a sport from the short list you cited, and not the entire 40+ types enumerated in the current FIT SDK.