If you have confidential compute(Intel TDX or AMD SEV) available from the cloud provider then it is feasible, provided you trust the CPU manufacturer. They should provide capabilities that allow you to perform remote attestation and ensure the virtual machine is running in the protected mode. Hypervisors running these types of machines usually can't access the memory of the virtual machine, not even the registers.
Of course, nothing guarantees there won't be a vulnerability that breaks it(e.g. side channel attacks), but right now the technology exists where you can run software in the cloud, protected from the provider..
What's wrong with gitea?