There are some DevOps capabilities that would really help your situation.
First a foremost, the original idea behind DevOps is that developers and operations collaborate the whole time. If you have a development team working in isolation of the operations team, it's definitely not DevOps even if they have been named "DevOps".
Let's get into some capabilities. I'm going to hand pick some specific techniques and practices that I think would really help future work in your organization.
Culture: Westrum organizational culture
Quite a lot of your original question involves blame. DevOps really needs a generative culture. That means a blameless culture with high psychological safety. You need to build trust, maximize learning, and aim to have people who are satisfied they can do good work.
This is one of the top-predictors of successful outcomes.
You may not be in a position to re-wire the organizational brain, but you can definitely make an impact with how you respond to your situation. Rather than looking for someone to blame, work out how you can collaborate with those other teams to get better results next time. A bit of empathy and relationship building will go a long way.
Lean product development: Work in small batches
If there is one universal lesson that came out of phased software delivery, Agile, Lean, and DevOps... it's work in small batches.
Imagine you had created a minimal .NET application in the first week. It just has one API endpoint that returns "hello world". If you delivered that version of the application you might have found out about the .NET version issue a year earlier.
Imagine the difference in finding out a year ago, rather than when you are about to go live. The situation wouldn't have blown up as the pressure to get things live is adding pressure.
Working in small batches would also mean having a deployment pipeline that you and the operations team had confidence in as you would have been deployment every week for a year.
Technical capabilities: Continuous Delivery
This is really a number of capabilities all bundled together - but they are highly inter-related. Frequent integration of code into the main branch and an automated deployment pipeline that make your code "always ready to deploy" are a great way to remove the stress from software delivery.
In your case, building the deployment pipeline would have meant collaborating with the ops team earlier and finding out what kind of governance, risk, and compliance needs they might have.
A good build process and automated deployments will boost your levels of joy. It will also enhance confidence in your team if you can make this area pain free.
You can explore more capabilities on the DORA research site. There's a lot of research and analysis that give us confidence in the relationships in the model.
Upgrading the .NET version shouldn't be too tricky. I've updated .NET Core MVC sites to .NET 6 and it none of the code needed to change. I tend to update regularly, so I'm now using .NET 7, but you may want to stick with .NET 6 as the even numbers have 3 years of support. The odd numbers have only short term support.
I hope you can get your API updated and get it launched. Now is the time to introduce some kind of continuous improvement process to make things better going forward. Once the dust settles and the crisis is over, people will be less willing to change the status quo.