Finally saw that there is "Microsoft Reporting Services Projects 2022" available for VS2022, which should by idea work as a report designer and open the existing reports. But it turns out all of the report projects now are unsupported/incompatible due to new version of VS. If the VS2019 will be installed, there everything will work.
And migration report is not very informative:
The application which this project type is based on was not found. Please try this link for further information: https://go.microsoft.com/fwlink/?LinkId=661331&projecttype=F14B399A-7131-4C87-9E4B-1186C45EF12D
Any ideas how to make them work in VS2022? Maybe someone had similar experience?
Solution: Thanks to the posted suggestion (marked green) managed to install 'Microsoft Reporting Services Projects' Version 3.0.1, which was crucial on VS2019, instead of the 'Microsoft Reporting Services Projects 2022'. That fixed my reporting issue, but due to outdated reporting solution. Probably will need to update it to newer one to avoid such legacy workarounds.
If you'd like to have early access to VS2022 release candidate builds before they are published to the VS Gallery, we’re making available to give customers an opportunity to provide feedback prior to finalizing releases. To access the release candidate of the extensions in Visual Studio, you may do so by creating a “private gallery” and entering the following settings.
Navigate to Tools > Options and then select Extensions and Updates under General. Under "Additional Extension Galleries", enter the following details: Name: Microsoft BI VSIX Preview URL: http://aka.ms/ProBI-VSIX2022 After entering these settings, your "Extensions and Updates" dialog will show updates for the extension when there is a new release candidate that you can install to provide feedback for a day or two before the VS Gallery VSIX is updated.
Provide feedback and report issues with this Vsix Package or Reporting Services projects in general to: ProBIToolsFeedback@microsoft.com.