Why has the "Ubuntu app" full access to my Google account?

"Why does Ubuntu have full access to your Google account?" Well, the answer is quite obvious here. You did not remove the specific access from within your Google account before installing the system.

Additionally, the entry gets created when you sign in to Google from within the Chromium browser; as Chromium is part of Ubuntu when installed from the repos, it shows as Ubuntu in the Google account.

On other Linux distributions the entry gets named in a different way, for example, when you sign in to Google with the Chromium browser on Fedora, the entry getting created is called 'Chromium Fedora'.

The reason why it shows a 'http' entry might be, that the web address that is relevant for the account setup is (still) not 'https' by default. Anyway, nothing to worry about - there is no malicious code at all.

When you want to revoke the access, just open "My Account" in a web browser, go to tab "Sign-in & security", go to "Apps with account access" and then click on "Remove Access" in the Ubuntu entry.

Of course the entry gets re-created once you sign in again with Chromium and grant the application access to your Google account. Please note that it happens by design and so is expected behavior.

Disallow Chromium itself from logging into your Google account. If you don't, simply logging into any Google App will also log Chromium itself into your google account with full access.

I suspect, if you are logged into your google account, with your web-browser itself (and not just at the web page-level), that would be a huge step toward facilitating Google to monitor all the non-google sites you visit. I'm sure the angels at google would never think of that, but I'm just saying that browsing the web with a web browser that's logged into Google seems closer to this possibility than browsing the web with a browser not logged into Google (at the browser-level).

To disallow, see first red box below:

After this, go here and remove any 3rd Party applications for which you do not want to grant google-account access: https://myaccount.google.com/security-checkup/

Additionally, if you care about privacy, I'd advise you to read each and every setting in the screenshot above (in your own Chromium) and always review them each time you install Chromium.