I recently acquired the .com version of my site’s URL (it’s currently on a .co).
Is the process for getting this new URL working correctly from an SEO perspective really simply connecting the URL and setting it as the default, as the support page suggests?
The .co version of the site is large and has acquired a good number of natural backlinks, and I was expecting to have to figure out a more detailed approach with a whole bunch of page level 301 redirects. Is that approach really not necessary here?
For example, if someone goes to page (dot) co/url-slug, they will be 301 redirected to page (dot) com/url-slug instead?
Yep. In this scenario the SEO value-transfer is trivial because it’s 100% the same site, and the only difference is the domain name.
When you add your new domain and set www.newdomain.com as your default, all requests to www.olddomain.com will be 1:1 redirected, and Google will update its SERPs over time.
Note that when you do this, you’ll want to;
Create a new google search console property for the new domain
Register your new sitemap URL
And if you’re running any paid advertising like Google adwords, you’ll likely need to update those URLs as well as it won’t follow redirects as an anti-abuse safety measure.