Do you ever run into performance issues with the shared machines at the low end? I've found the shared CPUs can be a little iffy under load but if you're basically running reverse proxying only it must not be an issue
Also do you think you'd pay $40/year? that's less than what you're paying Hetzner for no management.
I've been running stuff like code server [1] for some workshop I held recently and I was building simple .NET projects there without any issues.
I wouldn't pay $40/year because the value of having a random instance up with domain/ssl and nginx running all the time has been handy many times so far - worth way more than what I pay for the machine. At this point ngrok would be a downgrade for my use case, but if it was something like 20$/year when I was looking into it I probably wouldn't have bothered setting it up.
Also do you think you'd pay $40/year? that's less than what you're paying Hetzner for no management.