I think the name Eastside was used when the council were trying to identify their plans for the city for the next 20 years.
They came up with a "Big City Plan" and called others areas Southside (near the Hippodrome Theatre and the Arcadian), and also Westside (West of the city centre).
They also had others areas called "City Centre Core", "Digbeth", and "Jewellery Quarter".
https://en.wikipedia.org/wiki/Big_City_Plan
The Eastside area is also sometimes called the "Learning Quarter" as of course Aston University occupies much of it, and the Thinktank museum is there.
Also Birmingham City University (BCU) have new buildings there, and so do the Birmingham Ormiston Academy (BOA).
It has also just been announced that the Birmingham Conservatoire music school will also move to Eastside from its current site next to the old Library. The conservatoire will be knocked down, as well as the old library, as part of a massive redevelopment of the area. More here:
https://www.bcu.ac.uk/pme/conservatoire/news/new-home-announced-for-birmingham-conservatoire
It has also just been announced that they are going to build more student flats alongside the canal in that area, as part of the Eastside locks development.
https://www.alumnodevelopments.com/projects/east-side-locks-birmingham/
So there is still a lot happening in Eastside.
And of course if HS2 happens the huge HS2 station will go in that area.