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 That fixed my reporting issue, but due to outdated reporting solution.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.