How do I copy a SQL Server Database Schema and Objects between servers using VS2019
not exactly database project solution, but might be able to help you out with the filegroups if you don't find any other way.
dbatools offer this function - Export-DbaScript.
With that, you could try to export any object you want using SMO.
# set the option to not include Filegroup information
$options = New-DbaScriptingOption
$options.NoFileGroup = $true

# get all the tables from MyDatabase on the localhost
# generate script using $options defined above
Get-DbaDbTable -SqlInstance localhost -Database MyDatabase | Export-DbaScript -ScriptingOptionsObject $options