So on my note 10+ 5g, the bars represents my cellular reception. And I get an up and down arrow on 4G. So I think you might be looking at your cell reception rather than internet.
You realize, of course, that you must have cellular signal to have working mobile data (internet).
So, the stronger the cellular signal, the faster and more functional the internet should be.
At least in theory.
As OP mentions, the cellular signal is adequate, yet the internet is still inaccessible.
This is the exact problem that I have as well.
Not only that, my cellular signal is generally (much) worse than with other carriers as well.
T-Mobile ought to have an advertising scheme centered around 'Roaming At Home', as my device is almost always roaming.
Of course, whenever it is roaming, it is even more difficult to get internet service.
I really wish T-Mobile would just go out of business- their service has brought their customers back to the dark ages of cellular.
Maybe they will bring out a 'brick' phone next?
Of course, it wouldn't work as good as the original ones...