Don’t argue with him, provide numbers for the perspective he might not see. Tell him you want to help him make the best decision. He might loosen up on budget for cloud if he see that you are fumbling around to save a few Go of RAM.
Even a spreadsheet with such numbers is primarily speculation and your upper management knows this (they make such things all the time). As such, if they did not want to agree with you before this spreadsheet won't make a difference. If they want to agree but don't want to take the time to present exactly that spreadsheet to their compatriots, it is worth making it. If you don't work for a very large company (essentially a bureaucracy), this situation probably will not occur.
Also, while cloud pricing can be daunting, once you reach a point when Azure costs to much, you can look at optimizing things. There are a lot of techniques to keep cloud cost acceptable. Look up "FinOps" if you haven't already.
Your solution is to spend time and money on reducing costs. This only makes sense when the costs to move outweigh the costs to reduce costs.
- You ignore resource usage and move to dedicated hosting. You are now wasting money on inefficient processes. To remedy this you apply software engineering practices to understand the model and design it correctly.
- You ignore server unit costs and stay on cloud, but improve your runtime characteristics. You are now wasting money on the hardware, but your software is efficient. To remedy this you have to learn how to manage infra and take it on as constant maintenance.
It seems on your team it makes more sense to me to just pay for the cloud and stay in your software wheel-house.
But it sounds like your boss has the idea cloud is where it's at, it's hard to shift. I'd put numbers on it like how many less connections the cloud he wants to pay for can handle, vs the hosted solution for less $$$.
There is a line between premature optimization and total resource ignorance.