Thank you to everyone who responded and back advice / feedback! An update on the situation... Hopefully this will be helpful for anyone else that runs into my situation in the future on what to do / expect.
I contacted MNAO on May 9th and started an After Warranty Assistance claim. Here is the canned response to getting this started:
"Thank you for contacting Mazda Customer Experience Center. My name is Yarelis, case manager from Mazda CEC. I tried contacting you and left a voicemail. I am sorry to hear you are having issues with your CX-5 2019. We have contacted the Service Department regarding this concern and discussed assistance, I wanted to provide you with some information. Mazda is reviewing assistance for cylinder head repairs since there is a Service Bulletin, however for any After Warranty Assistance there must be a customer participation and the dealership warranty team would provide the coverage amount based on dealer diagnosis. At the moment the dealership have not determined if this issue is related to the cylinder hear or an engine block so a claim can not be submitted, Jeff at the service department explained they have to have your approval and permission to go into detailed on the diagnosis since that is a 18 hours of labor. Mazda can not review assistance for repair unless we have a detailed diagnosis done by the dealer. If you would like After Warranty Assistance to be reviewed please contact the dealership and discuss diagnosis information with them in order to proceed. Since the vehicle is outside of warranty we are unable to assist with diagnosis, but because you are a value customer, if the diagnosis determined to be an issue related to a recall or a service bulletin Mazda will review assistance towards a percentage of the repair. Please let us know if you have any additional questions!"
This meant I was required to agree to the $3200 (18 hours) of work to do the engine tear down. My decision was that even if I did have to incur the the cost of a new engine ($10k estimate per dealer; including the $3200) this would be a preferred alternative to purchasing a new car or even used car. This has been the first major issue I've had during ownership. I have taken my vehicle to the dealership to have all maintenance work done and have performed all dealer-recommended service; MNAO could see this and verified this during the initial call with them.
Early during the week of May 15th the dealership let me know that they didn't see a crack in the engine block, but were doing more diagnosis work to verify what the issue was exactly. I had a planned vacation where I would be out of the country from May 18th through May 23rd and let them know I wouldn't be reachable during this time.
After returning home on May 23rd, I had the following message from MNAO CEC (sent on 5/23):
"I am following up with you regarding your case. Jeff from the service department followed up with me regarding the diagnosis. He will be submitting a claim for after warranty assistance, however his warranty administrator will be out of the office till Tuesday the 30th. He will have to wait to submit till then. I will also be out 30th till the 8th. Dealer will be contacting you with warranty decision on coverage. I will also be following up with you after with repair status. If you have any questions or need any additional assistance you can also contact 1-800-222-5500 while I am out of the office. Please let me know if you have any questions or concerns."
I spoke with the dealership on Friday May 26th and they provided the diagnosis of needing a Cylinder Head Replacement, which they were going to request be covered 100%. In addition to pre-authorizing the Cylinder Head, they also requested a new Manifold and Turbo Engine due to "coolant gumming them up". They said they couldn't guarantee that MNAO They said they responded to the After Warranty Assistance claim and recommended based on my service history and being a good customer that the cost be covered 100%, which was great news to hear!
Based on the email from MNAO CEC and everyone being on vacation, things stalled from here. I tried reaching out to get an update via email on 5/31--no response. I called MNAO yesterday (6/5), twice, asking for an update. I was first told that the person assigned to my case would be in contact with the dealership later in the day. I called again after 5PM and was told that the agent assigned to my case would review what was submitted by the dealership and respond tomorrow (6/6). Apparently they don't know how to use out of office responses to let people know they're on vacation.
I called MNAO today (6/6) and requested to be transferred to the person managing my claim--they weren't in, which again wasn't a surprise by based on the email saying they'd be out until the 8th. I am now going through the hoops of trying to get another case manager to review the case before the assigned individual returns on the 9th. I'll have to call back again tomorrow when managers are available.