I don’t know how many more qualifying rounds there are, but it can’t be possible for the tournament to be played with this many teams. From what I can tell, I think there will be a playoff round after this one, and the teams that advance from that will compete in the tournament. Right now, I don’t even know who most of the teams playing in the qualifiers are. Teams like Panathinaikos, Dynamo Kyiv, and Braga are the only ones that catch my eye.
After this round there will be play-off stage. You will see teams from Europa League then. When they lose in the 3rd qualifying round, they'll be relegated to the Conference League play-off stage.
In addition to that, teams eliminated in the Europa League play-off round will qualify directly for the Conference League group phase.
So a few more relatively strong teams will be joining this league.
Financially there isn't much difference between the Conference League and the Europa League, but in terms of quality there's a huge difference. That's why I think Turkish teams have a better chance in the Conference League. Unfortunately Başakşehir weren't able to take full advantage of that. If the Top 4 were to play in this league one day, their chances of success would be very high.