Powershell and regex: List of Notepad++ "backup on save" files. Edit name, sort by lastwritetime

I'd use a RegEx with zero length lookbehind assertion to remove everything after html from $_.Name

This can be done with a calculated property either in a Select-Object or also in a Format-*

Get-ChildItem -File | 
  Format-Table @{n='foo';e={$_.Name -replace '(?<=^.*\.html).*$'}},Name -HideTableHeaders

Sample output:

available13.html available13.html.2019-03-26_081523.bak
index.html       index.html.2019-03-26_081538.bak

You can add a new property with Add-Member like this

$time = (Get-Date).AddDays(-4)
$files = gci * -include index*,avail* | where {$_.LastWriteTime -gt $time}
foreach ($f in $files) {
    $f | Add-Member noteproperty newName -Value `
             $f.Name.Substring(0, $f.Name.Length - ".yyyy-mm-dd_iiiiii.bak".Length)
}
$files | Format-Table -HideTableHeaders newName,Length,LastWriteTime

Note that the above snippet assumes that your names always end with .yyyy-mm-dd_iiiiii.bak. If they have some other format then you must include that information in the question, and you may need to use other string methods like replace, substring... to remove the unnecessary part