Germany is facing difficulties in taking in more migrants, President Frank-Walter Steinmeier said on Wednesday.
“Germany, like Italy, is at the limit of its capacity,” Steinmeier said in an interview with Italian Newspaper Corriere della Sera, pointing out that Germany had received a third of all EU asylum requests in the first half of 2023.
The president acknowledged that both Italy and Germany had “heavy loads to bear” and called for a “fair distribution” of migratory burdens within Europe.
You're conflating asylum with immigration.
Almost all migrants call for asylum, and it's then on the country to process it and evaluate if it is true. In that time, typically the asylum seeker will be able to stay. There is afaik no reason not to request asylum. So the two are very much linked in practice.