Use "webnavigation" and direct it to the extension page...

Were you able to get this to work? chrome.webNavigation.onBeforeNavigate doesn't fire when a new start page tab is opened with ctrl + t or the + button on the tab bar. If you navigate from another page view, the start page button or entering the URL, it'll fire though. So, it'll only work part of the time.

chrome.webRequest.onBeforeRequest doesn't fire for the startpage, so you can't block it and then use redirectUrl with it.

This method works, but it has a few downsides. The history issue could probably be fixed with the history api though, but haven't tried.

"permissions": ["speeddial"],

https://dev.opera.com/extensions/web-navigation/
https://developer.mozilla.org/en-US/Add-ons/WebExtensions/API/webNavigation

I guess this is defunct?
https://dev.opera.com/extensions/speed-dial-api/
https://dev.opera.com/extensions/speed-dial-manual/
Or is it? That dev page seems like it needs an update.

In the extension's manifest file is:

"chrome_url_overrides": {
  "newtab": "newtab.html"
}

But, that doesn't do anything as Opera's new tab page is "startpage" instead. But, if I change "newtab" to "startpage", I get the error mentioned in the OP.

I can work around it by closing Opera and editing its preferences file. This needs to be under "Extensions".

"chrome_url_overrides" : {
  "startpage" : [
     {
        "active" : true,
        "entry" : "chrome-extension://llaficoajjainaijghjlofdfmbjpebpa/newtab.html"
     }
  ]
}

However, in Chrome, that gets created automatically (with "newtab" instead of "startpage" obviously). In Opera it doesn't.

So, I'm not sure if Opera actually supports the override from the manifest file.

In the Opera version of FVD speed dial (which isn't kept up to date I think), I see a workaround in "js/bg/newtab_replace.js" which just replaces Opera's startpage tab every time one loads with the extension's newtab.html page.

In short, I would guess that Opera is blocking the override from the manifest file.