I'm not sure what you mean by mediatic evidence. Before and during the recent run-up, their were reports all the time about grayscale trust buying bitcoin. You also had Microstrategy very publicly share their stance that they won't be holding their reserves in cash but are instead using bitcoin as their reserve asset.
There was recently a company, Capital Group (never heard of them before this announcement), that bought a small double digit stake of Microstrategy.
That all said, for any large buyer, it's in their best interest to not advertise they plan on buying anything, much less bitcoin. It's actually in their best interest to spread as much negativity as they reasonably can about whatever they're buying.
I personally wouldn't use news stories about institutional adoption as an indicator of anything. By the time any significant market moving news reaches you or me, the larger players are closing out their trades.
As for why I personally believe Bitcoin will continue appreciating, adoption is still very limited, so there's much more room to grow. Additionally, the only fundamental change to Bitcoin since the recent run-up was the banning of mining in China. Miner concentration in China was always a criticism of Bitcoin, so we will see how this ultimately plays out. Best of luck to you.