URL Rewriting

I have no experience with rewrite profiles, but I may be able to help with that iRule.

Your condition only matches when the path equals /webapp/, but you want it to match when it starts_with.

Then after that it would rewrite the entire url to "/", not just remove the /webapp/ portion of the path.

Instead you should be able to almost 1:1 use this example from here https://devcentral.f5.com/s/articles/irules-101-14-tcl-string-commands-part-2

when HTTP_REQUEST {
   set uri [HTTP::uri]
   if { $uri starts_with "/axess2" } {
      HTTP::uri [string range $uri 7 end]
      pool pool1
   }
}

Adjusted to your own example:

when HTTP_REQUEST {
    set uri [HTTP::uri]
    if {[string tolower [HTTP::host]] eq "www.myweb.com" && [string tolower $uri] starts_with "/webapp/"} {
        HTTP::header replace Host "app.myweb.com"
        HTTP::uri [string range $uri 7 end]
    	pool new-web
      }
    }