As I wrote already, if an app needs this level of babysitting, fix the code and/or the infrastructure. If having people on-call 24/7 seems normal to management, they need to step up and address the bugs, failures, downtime, and the lack of redundancy, monitoring, and automation. I would strive to get the support burden down to a very occasional alert on my phone that I can respond to from my phone.
When I see this kind of thing with my customers it comes from a combination of unrealistic expectations ("We need 99.9999% uptime for our marketing sites") and over-engineered and fragile infrastructure, code, and development/deployment processes ("Our K8S/microservices architecture can fail in many ways that no one understands.")
I did some work for a company a few years ago that had a cron job that rebooted the web server every day, because that was the solution they had come up with to "fix" the server crashing (Apache + Rails in that case). The actual problem was running MySQL and Apache on the same server, leading to MySQL eventually starving Apache for memory. Once I fixed that Apache + Rails would run for years without needed a reboot. I had another customer with a server that ran out of disk space every couple of months, requiring frantic resizing of an attached disk. Moved them to S3, problem solved, no more calls.