Humble request. I listened to Duolingo and Farvo pronouncing it
https://forvo.com/word/comhghairdeas%21/#ga
I hear: co-ghoar-jes
Could somebody throw a couple kind pointers my way what is
happening here?

What do you mean in particular?
It is pretty much pronounced as spelled.

comhghairdeas /koˈɣɑːɾʲdʲəs/

comh /ko/ (mh silent)
ghair /ˈɣɑːɾʲ/ (a: one probably would expect a more frontal a /æ ~ a/ [as it is in Ulster pronunciation] but it is a back a /ɑ/, "silent" letter i is due to palatalized ("slender") r; stressed syllable because comh is just a prefix)
deas /dʲəs/ (silent letter e is due to palatalized d, a is pronounced weakly as /ə/)

You can listen to teanglann.ie, too
https://www.teanglann.ie/en/fuaim/comhghairdeas
(it is comhghairdeachas in the Munster version)

It is actually comhghairdeachas in Conamara too.
But I pronounced it as standard there.

Yes, I am Bríd Eilís too.

I can redo the word for both pronunciation.
I don't know how it's said on Duolingo.

Oh wow! https://forum.duolingo.com/comment/4293825
Duolingo pronunciation sounds very Connacht to my ears.
And so is Forvo - unless they (my ears) need more tuning.

Here is Duolingo - I hope that link will work for you. Audio is
on top of the page (it is easier to link to comment page than main).
https://forum.duolingo.com/comment/4293825

Thank you very very much.
Both for detailed explanation and for the http://www.teanglann.ie link.
I am just starting so it is like English person staring at Polish word
"Szczęście" (happines, luck). And even then it is easier because
pronunciation is more or less uniform across Poland (accent may
slightly vary). So getting a small foothold really helps.

And I think I need to be very careful at this point and re-check all words -
Duolingo to my ears pronounces it the Connacht way. Even though
they supposedly teach Munster.

Edit: OK so I was corrected by Mod person and Duolingo indeed teaches
Connacht.

The Standard/Caighdeán is a mixture of Connacht and Munster spelling and grammar. There is little or no Ulster included. There is no standard pronunciation, if there were natives would be raging, imagine telling a person from Donegal he must pronounce like a Galway person.

When Irish Duolingo started the speaker wasn't native and people were complaining about the pronunciation, fair play to Duolingo they replaced her with a native speaker from Connacht. Then other people were complaining as they couldn't understand native speech, especially Irish people who only knew non-native school Irish. I haven't been on the Irish section in a long time, so I don't remember if she pronounces the way it's written or uses native pronunciation, like I did with "comhghairdeas". Learning to read Irish can screw up your thinking.