The variables are one char long due to my original limitations of the script lenght, sorry for that. the commentaries I added later

AutoIncrement_AndroidManifest.ps

#Path to the AndroidManifest
$p="path\to\manifest\AndroidManifest.xml"

#Get the content of the file
$f=Get-Content $p

#Describe the pattern to search to edit the versionCode with RegEx
$r=@"
android:versionCode="\d+"
"@

#Get the part of the file's content that matches the RegEx
$v=[regex]::matches($f,$r).Value

#Take the part of interest (versionCode),
#search for any consecutive numbers as string and convert it to int
$v=[int]([regex]::matches($v,"\d+").Value)

#increment it
$v++

#Execute a
#  foreach line of the original file's content
#      search for the regex pattern
#      substitute the original number with the new one
#  save the new content to the "$c" variable
$c=$f|ForEach-Object{ $_ -replace $r, @"
android:versionCode="$v"
"@}

#Save the edited content to the original file
$c|Set-Content $p

#Print out the result for debbuging proposes
echo $c