This is true, but I am afraid only for your expectation (no offence, might be a bit misunderstanding of the terms used here).
Using Transform Rule → Rewrite, you will see “old” URL in your web browser, while the main task and the thing is done and working “behind the scenes” as it is supposed to.
That’s how URL Rewrite works.
You won’t see the new modified URL in the URL address bar of your Web browser.
Yes, but if you made a rewrite, then the correct thing is done in the background.
Check HTTP headers via Dev tools (F12) or curl.
Redirect is not the same as Rewrite.
Redirect/Forwarding - This is a server-side response that tells the client to go to another URL. This means that the URL displayed in the browser’s address bar gets updated to the new URL
Rewrite - This is a server-side modification of the URL before it is fully processed by the web server. This will not change what is seen in the user’s browser.
May I share a recent post below, as from what I understand what you are trying to achieve it is related to the same.
Using Page Rule:
Just in your case, https://davidleesmith.com/collections/tools/* first field and https://david-lee-smith.myshopify.com/collections/tools/$1 in the second field while using Page Rules.
→ or maybe just https://david-lee-smith.myshopify.com/collections/tools/ in the second field (in case you do not have any “old” URLs and don’t want to follow URL path from “old” to the “new” one)
Otherwise, please reply so we could troubleshoot or help more.