You can use ConvertFrom-StringData to convert Key=Value pairs to a hash table:
$filedata = @'
app.name=Test App
app.version=1.2
'@
$filedata | set-content appdata.txt
$AppProps = convertfrom-stringdata (get-content ./appdata.txt -raw)
$AppProps
Name Value
---- -----
app.version 1.2
app.name Test App
$AppProps.'app.version'
1.2