Personally, I do care that cloud is in the order of 10x the price and do have to explain infra cost as a metric of our road to profitability to our board.
My company does work closer to the metal, especially because for us the notion of “scaling” is not that we can simply slap a load balancer or a cache in front of a bunch of servers and call it a day: when you work with HFT or AAA Games: the performance you get on a single machine really matters, as does the ability of that machine to work reliably since there is state.
People in HFT and games really bleed for people like you and I, since its not as simple as CRUD stateless HTTP stuff where performance is measured in milliseconds and the average node runs 2GHz on all cores with 14 different abstractions.
Cloud optimises for the web, when its not the web, there are major dragons- those are your people.
The one area where you might want to focus is HPC. All the companies building huge GPT models need highly optimized hardware.
The only question is whether pushing for working things instead of nice talk will get enthusiastic support or opposition from the management.
I don't think you should feel excluded from "Software Engineering" just because you don't have a passion for managing containers. We need people who can write great code in the world, too!