When I search replace in migrate db, is normally do the following replacements:
//url.example/wp -> //url.example
/app/ -> /wp-content/
For the second one url.example/app/ -> url.example/wp-content/ may be more appropriate
For the site files, I rename the app directory to wp-content and remove the bedrock-specific plugins from the mu-plugins directory. Eg bedrock-autoloader.php In our case we don’t have anything in mu-plugins relevant to no bedrock or non trellis hosting.
So the client gets a database and a compressed wp-content they can drop into a clean wordpress install. This way no bedrock-specific mu-plugins OR config comes across.