Handling Reporting Services and SharePoint Integration considering deprecation
Now our client wants SharePoint integration with Reporting Services

If they just want to embed reports in SharePoint pages, or write reports consuming SharePoint List Data, go with a native-mode installation of SSRS or Power BI Report Server and use the Report Viewer Web Part, or just the Web Page Web Part for embedding.
You might suggest they go with Power BI Report Server as it not only has the SSRS functionality, but also the Power BI Interactive Reports that are the successor to the old PowerView reports in SharePoint.
SSRS SharePoint mode adds the ability to deliver scheduled reports to SharePoint Lists, but there's reasonable workarounds for that in Native Mode.  And adds the ability to manage report content (reports, data sources, etc) inside SharePoint, so that's the key difference between Native and SharePoint integrated mode.  If they really need that, go with SSRS 2016.  It will be supported until July 2026.