I have some dynamic pages in my intranet website (CRUD operation plus search/filter). I have office 365 SharePoint online version. I want to develop client web part using reactjs and restAPI to work with my premise SQL server data. Is SPFx client webpart durable? Also how robust it is to achieve CRUD operations and filter/search using RestAPI development? I also might have to access the sharePoint files stores using SharePoint RestAPI or other methods if available. But most of the time I will be using my premise SQL server since I have lot of procedures already working in place.
You should look at SharePoint provider hosted add-ins for your case. In this way you can deploy your add-in as Azure Web app, create a site-to-site VPN with your on-premises data center (unless express route already exists in your environment) and use SQL server on premises data in your add-in through hybrid connection.
As per Microsoft, The SharePoint Framework (SPFx) is a page and web part model that provides full support for client-side SharePoint development, easy integration with SharePoint data, and support for open source tooling. With the SharePoint Framework, you can use modern web technologies and tools in your preferred development environment to build productive experiences and apps that are responsive and mobile-ready from day one. The SharePoint Framework works for SharePoint Online and also for on-premises (SharePoint 2016 Feature Pack 2 and SharePoint 2019).
Using SPFx you might be able to build the UI of your application and make use of SharePoint data, but you also need to think about connecting to your on-premises SQL Server database.
Otherwise you might have to think about exposing your SQL server data using a WCF service and make it available in SharePoint online through BCS, which will have limited scope to work with your data comparing to provider hosted add-in.