Can it be done in Classic?
Most likely yes.
There are limitations in any systems, and at present those are more prevalent as the API 28 compiler is buggy and cannot handle 1/3 the size code that the previous API 26 compiler had no problem dealing with. And even the API 26 compiler had limitations, not to mention that the concept behind Thunkable is that of a meta language that gets interpreted, as opposed to being directly executable.
So, it can be done.
The issue is: is it desirable?
And that seems to be no.
Sure, you want to wedge your own ads in there and profit from it. But what on Earth are you giving extra to the USERS?
I already have a browser in my Android devices, why should I add another layer so that YOU can profit from it?
Will the access be faster? No, on the contrary, you would be adding your own processing to add your own links.
Would it be easier, more user friendly? Does not appear that it would.
So, what is in it for the user?
Then this ‘app’ of yours is worthless for the end user. And apps that do not give any value for the users are not acceptable by play.google.
Last point I got reading your “my ideas” text: you need to undergo a serous ego deflation process. You write it as if you are the greatest thing since sliced bread, yet have nothing to show for yourself. A bit of humility would serve you better.
Even the handle you selected for yourself (“super.apps.builder”; seriously?) reeks of unjustified arrogance.