How to convert classic sharepoint online project site to modern site?

Invoke-SPOSiteSwap is a SharePoint Online PowerShell cmdlet that can be used to swap out your old classic SharePoint root site in your Microsoft 365 tenant and replace it with a shiny new Modern Communication Site ,Modern Team Site or Classic team Site (Invokes a job to swap the location of a site with another site while archiving the original site).

For more details refer this blog https://regarding365.com/invoke-spositeswap-a668bcad4e9b

Or

one more workaround Convert Classic root sites to Modern SharePoint

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Modernize your root site (Microsoft Documentation)

1. If you have a different site that you want to use as your root site (a communication site or modern team site that isn't connected to an Office 365 group), replace (swap) the root site with the other site.
2. If you want to keep using the classic team site but add a new modern home page and enable full-width pages with horizontal navigation, enable the communication site experience on the site.
3. If you want to continue using the classic team site, enable the modern site pages library experience and set a modern page as the home page of the root site. This gives users a modern team site experience with the left navigation.

You could take a look at this:

https://docs.microsoft.com/en-us/sharepoint/dev/transform/modernize-userinterface-site-pages-powershell

Pnp powershell code for your reference:

$userName = "username"
$passWord = "password"
$encPassWord = convertto-securestring -String $passWord -AsPlainText -Force
$cred = new-object -typename System.Management.Automation.PSCredential -argumentlist $userName, $encPassWord

Connect-PnPOnline -Url "https://contoso.sharepoint.com/sites/SharePointRNDClassic" -Credentials $cred
 
#Using the below command converting the classic "home.aspx" page to modern page and adds the page accept banner web part on top of the page.  
ConvertTo-PnPClientSidePage -Identity home.aspx -AddPageAcceptBanner