0.910 --install-types doesn't install stubs for 2nd level deps on first run

Bug Report

I use mypy in CI for a library, that depends on aiochsa. And aiochsa depends on backports.zoneinfo for python prior to 3.9. The first run of mypy --install-types --non-interactive -p my_package (the cache is empty) in python 3.8 environment installs all needed stub packages, except types-backports, causing pipeline to fail with "Library stubs not installed for "backports" (or incompatible with Python 3.8)" error. The second run of the same command installs missing types-backports and pipeline succeeds.

Expected Behavior

mypy --install-types --non-interactive … installs stubs for dependencies of dependencies on the first run (with clean cache).

Actual Behavior

mypy --install-types --non-interactive … installs stubs on the run for 1st level dependencies only.

Your Environment

• Mypy version used: 0.910
• Mypy command-line flags: --install-types --non-interactive -p …
• Python version used: 3.8

Reproduce the issue with mypy 0.910 using Python 3.8, an empty cache, and mypy --install-types --non-interactive -p my_package. Trace the --install-types entry point and dependency discovery for aiochsa and backports.zoneinfo; done means the first run installs types-backports and the type-checking pipeline succeeds.