For completeness then, here's the news from Tweetium's developers:
Other functionality such as multiple account support will continue to work after that. However, at this time, most Windows users will want to check out Twitter's official app, as Twitter is making it impossible for other apps to continue going forward.— Tweetium app (@TweetiumWindows) July 29, 2018
In the Store, Tweetium's 'Pro' mode was offered as:
The Pro add-on service enables support for up to 7 accounts, push notifications (mentions, DMs, RTs, quotes, favs, and new followers), a richer Connect view powered by Tweetium Pro notification servers, TweetMarker sync, and integrated news reading powered by our other app, Newseen
Given that Tweetium itself is a commercial application, most AAWP users will, I suspect, be satisfied with the standard application and not 'Pro' subscribers. The reference to 'push notifications' is a little unclear. I think it refers to notifications on that wider range of events and that basic notifications of mentions and DMs will continue in Tweetium. But this might be wrong and maybe we won't know until Twitter's API changes are implemented.
If you are an existing Tweetium 'Pro' subscriber, possibly for the multiple account support, then this feature will carry on working, though what happens in a year's time when your sub is due for renewal is anyone's guess!
It's noteworthy that Twitter's API changes are affecting all mobile platforms, including iOS and Android - this, for once, isn't a Windows thing.
Twitter, having started out as being very third-party-friendly, has become increasingly hostile to clients over the years and this may be the straw that breaks the camel's back in terms of routing more people towards the official Twitter client for each platform. On Windows 10, it's a PWA and, while all very nice generally, notifications are non-existent on Mobile, which is a shame.
Can any readers shed any light on whether notifications will also stop for the main Tweetium app too?