My guess is when your text widget data is serialized in wp_options, it looks like this:
a:3:{i:2;a:3:{s:5:"title";s:0:"";s:4:"text";s:279:"<br><a href="https://myurl.com/page/"><img src="https://myurl.com/wp-content/uploads...}
So when it replaces out your new url:
a:3:{i:2;a:3:{s:5:"title";s:0:"";s:4:"text";s:279:"<br><a href="https://mynewurl.com/page/"><img src="https://mynewurl.com/wp-content/uploads...}
The character count changes (the 279 number), messing up the entire serialized data, in which wordpress them I’m guessing clears out if the values don’t match up with the char count?
It looks like if you choose the second option where you check all the boxes and do the replace in the plugin it works fine, since it doesn’t do anything to the wp_options table. You’ll have to just go into the sidebar widgets and any other options settings to do the replace manually