Hey!
Looking through the API fetch for the versions in the Updates tab, I noticed a section for release notes:

"releaseNotes": {
 "url": "https://storage.googleapis.com/live-platform-resources-prd/templates/assets/6000_1_0a2_aba23c7824/6000_1_0a2_aba23c7824.md",
 "type": "MD"
}

If we follow the link we can see that the entire file is markdown (also indicated in the json as well as the file extension). I think this would be a great way to easily display a popup-window inside the app, maybe even with a search bar. That way there's no need for a browser opening or anything to be opened separately.
I am also not sure if having both Release Notes and Cumulative Release Notes is that useful (Maybe allowing multi-select in the Updates tab and only then showing the cumulative button which would then open the website with the correct query).

Another way to fetch release notes which would also support cumulative ones is this API fetch from the actual website:
https://alpha.release-notes.ds.unity3d.com/ajax/search?fromVersion=6000020f1&toVersion=6000022f1
It returns a json instead of a markdown and looking at the javascript, they also do some processing to display it nice on the website. Should be easy to replicate, even though I find straight release notes in the app better, and the cumulative ones for the website maybe?