I found a solution that works for transferring Wordle data using this tool: https://sethmlarson.dev/blog/wordle-stats
This works great in any browser, but I found it a little tricky when dealing with a web page saved to the Home Screen, since the "Add to Home Screen" command does not copy over any storage data.
I was in a similar situation, trying to transfer my old https://www.powerlanguage.co.uk/wordle/ link (saved to the Home Screen) to https://www.nytimes.com/games/wordle/index.html.
Since the saved Home Screen web page doesn't provide you with an address bar to navigate to the tool mentioned above, you could tap the Settings (gear) icon in the top right corner of the newly added NYTimes Worlde saved web page, and follow the Twitter link, taking you to the @NYTGames account. From there, you can scroll down or search for this tweet: https://mobile.twitter.com/NYTGames/status/1532414444575375361
Alternatively, enter the URL for the Wordle stats tool in the "Search Twitter" input field, which should help you reach the page. The idea is basically to get to a tool such as the one mentioned within the newly added Home Screen site.
From there, follow the instructions on the site to reset your statistics. Note the one caveat that this tool currently is not able to reset your current streak.
EDIT: I found another similar solution, using the same concept of finding a way to navigate outside the saved New York Times site, but doing so by getting to Google and using different tool to fix, which purportedly allows you to set the current streak: https://www.reddit.com/r/wordle/comments/v15u3i/fixing_wordle_stats_for_those_who_have_ios/