So, regarding the landing page, we now have 4 icons inside the search bar.
One on the left side, and three on the right side, positioned on the same horizon level, one next to the other...
That is maybe a bit too much.
I thought about taking the 3 icons on the right side out of the search bar,
and putting them into "islands", that float next to the search bar...
Has a "nostalgic" y2k look on it, but I think it actually does its job.
You could make the buttons smaller, and move the higher / lower button a bit more to the right.
So they truly float around that rounded corner of the search bar.