I've published some instructions using the Reporting Services with Oracle Autonomous DB. The difference with on-premises DB should only be customizing the authentication features you use. The most likely step you are missing is running the OraProvCfg utility to register ODP.NET in the .NET configuration file. Here's the tutorial:
I recommend you use managed ODP.NET to make install and configuration easier. All ODP.NET19c versions support connectivity back to Oracle DB 22.214.171.124.
this isn't helping me much.
I still don't know which version of ODAC - or Xcopy as mentioned in your tutorial - should I install.
However I downloaded 64bit version as Win10 is 64bit and tried to follow your steps.
Unfortunally I didn't pass even step 1. Isn't there any simple installer file like "setup.exe" ?
In these days there should be something simple as this.
Any of the ODP.NET 19c versions will work.
Microsoft has a similar tutorial here covering the managed ODP.NET configuration part.
The Oracle tutorial is much more end to end, though it covers an Autonomous DB scenario.
To answer your other question, the ODT tools and Oracle DB Client installs use setup.exe or equivalent VSIX. However, neither performs the machine.config changes SSRS uses. In general, .NET data providers are no longer making automatic machine.config changes due to the global effect on existing apps. The preferred method is for developers to change the app's specific app.config file. However, that's only possible if the SSRS exposes a local app.config type file, which it does not.
That leaves customers with these instructions, which I agree can be clumsy to implement. However, SSRS is the outlier. It's not modernizing its data provider infrastructure to follow ADO.NET best practices. In fact, it's not clear when SSRS will support ADO.NET Core.