there is no webform support in .net core. you will need recode the webform UI code.
to start, you should move as much code out of the webform project into separate projects which you can upgrade to netstandard 2.0, and then after migration .net 8
to replace the webform code, you have two options.
the first is Razor pages, which is a template engine approach. there is no support for client events, you use a post back model. also as template engine, there is not the concept of a control tree like in webforms.
https://learn.microsoft.com/en-us/aspnet/core/razor-pages/?view=aspnetcore-9.0&tabs=visual-studio
the second is Blazor app. Blazor apps use Razor syntax, but builds a control render tree like webforms and supports client events. a Server Blazor app hosts a persistent connection (signal/r) to the browser, and has a dedicated application instance for each user. Blazor also has a client mode, but this builds a client SPA app like angular or react, but in C#.
https://dotnet.microsoft.com/en-us/apps/aspnet/web-apps/blazor
You didn't specify your language, but asp.net core only supports C# and F#. If you have VB code, it is only supported via referenced class libraries.
as webforms migration requires a lot of recoding, Microsoft has an incremental migration approach, using a reverse proxy. you basically run both the old site, and new site, but the proxy makes t look like one site. also session and authentication cookies can be shared between the two sites:
https://learn.microsoft.com/en-us/aspnet/core/migration/fx-to-core/?view=aspnetcore-9.0