This is a VE bug. Maybe the buttons should be reworded to something like: No, I don't want and Yes, post with my IP as that's what they really do.

The Editing team will take a look at this

@JTannerWMF any updates on this? It's been almost 2 years :)

Change 876340 had a related patch set uploaded (by Nardog; author: Nardog):

[mediawiki/extensions/VisualEditor@master] Show "Continue" instead of "Try again" on button to save as another user

https://gerrit.wikimedia.org/r/876340

Test wiki created on Patch demo by Nardog using patch(es) linked to this task:
https://patchdemo.wmflabs.org/wikis/13fb1c454e/w

It's regrettable that the Continue button is still the one that's emphasized, but it's at least better than "Try again".

While better, this may still not be easily understandable by a user. I think the best thing would be to change the labels (as mentioned in T190406#6063318). If that is too much work (looks like a generic error dialogue is used here) I think at least the word "continue" should be added to the message, e.g. "Do you want to continue and save this page[...]".

Change 876340 merged by jenkins-bot:

[mediawiki/extensions/VisualEditor@master] Show "Continue" instead of "Try again" on button to save as another user

https://gerrit.wikimedia.org/r/876340

Changing the label of the buttons would be too much work. The related line is hardcoded here and there's no easy way to override it. Changing the message given to the user is much more possible, and since HTML is parsed in the latter portion of that message, we can add emphasis where needed. The message in that case would be:

We could not save your edit because the session was no longer valid. You can try again by saving this page as an anonymous user, but your IP address will be recorded in the page's edit history.

The related message changed above is here for reference. The change above follows the same sentence type of its counterpart (visualeditor-savedialog-identify-user), which uses a declarative statement instead of an interrogative one.

Thanks for the patch!

Changing the button labels and styles is a bit tricky, but possible. The error interface is implemented in OOUI and not easily customizable, but like most things in OOUI you can just override the method that displays it.

Here's an example of doing that I just found: https://gerrit.wikimedia.org/g/mediawiki/extensions/TemplateWizard/+/08db935590faaf907cc22b4f5ba861f1dead1a9f/resources/ext.TemplateWizard.Dialog.js#128 (and some more different examples: https://codesearch-beta.wmcloud.org/search/?q=.prototype.showErrors)

I'd be happy to review a patch if you submit one.

Test wiki on Patch demo by Nardog using patch(es) linked to this task was deleted:

https://patchdemo.wmflabs.org/wikis/13fb1c454e/w/