TL;DR - using Incognito Mode offers more privacy in the google Chrome browser than not using it. The feature is intended to hide your actions from those who share your machine, but does little to hide you from the all-seeing googly-eye.
Does Google collect and store any data about this activity ("watched videos on Vimeo" activity)?
In general, does Google store ANYTHING that is done in Incognito mode?
Private Browsing systems are generally built around the concept of hiding your history from your machine. Not on stopping the flow of valuable information to google. If you have 'SafeBrowsing' enabled for example then effectively the URLs you visit are sent to google even if they aren't logged in your history.
Google's Chrome Browser Policy for incognito mode is conspicuously silent on Installation Tracking, Promotion Tracking, or Field Trials, all of which send potentially personally identifiable information to them.
How Chrome handles your incognito or guest information
Cookies. Chrome won't share existing cookies with sites you visit in incognito or guest mode. Sites may deposit new cookies on your system while you are in these modes, but they'll only be stored and transmitted until you close the last incognito or guest window.
Browser configuration changes. When you make changes to your browser configuration, like bookmarking a web page or changing your settings, this information is saved. These changes are not affected by incognito or guest mode.
Permissions. Permissions you grant in incognito mode are not saved to your existing profile.
Profile information. In incognito mode, you will still have access to information from your existing profile, such as suggestions based on your browsing history and saved passwords, while you are browsing. In guest mode, you can browse without seeing information from any existing profiles.
This does not include the myriad of other google services which may give less detailed (but still very useful) information such as google DNS and DoH.
For all their talk, google are serial privacy abusers. In the last 12 months they've come under fire for attempts to track users between sites without 3rd-party cookies, collecting personal data without authorisation, failing to wipe cookies when told to, and privacy concerns in reCAPTCHA. Google's concept of privacy is that it is privacy from one another, not privacy from google.
As Eric Schmidt famously said...
If you have something that you don’t want anyone to know, maybe you shouldn’t be doing it in the first place.
CNBC 'Inside The Mind of Google'
...and that was in 2009. What makes the google search product (and powers their ad platforms) is really the amount of data they have on internet users.
It's also worth pointing out that switching browsers is unlikely to be that helpful as many browsers use the Chromium codebase. When Microsoft re-worked Edge to use the Chromium engine they had to alter or remove over 50 services that supply data to google.