Optimize PROD image caching in CI

[potiuk]

Turns out that some of the layers in our PROD image got invalidated because AIRFLOW_CONSTRAINTS_MODE used to build the cache for PROD image is "constraints" by default, while building images in "build-images" workflow for regular PRs and canary build uses "constraints-source-providers". The former is fine as default for PROD image (as oppose to CI image we build PROD image from released PyPI packages by default) but the latter is "proper" for the CI cache, because there, the image is built out of local packages prepared from sources.

Turns out that the CONSTRAINT_MODE parameter had a profound impact on caching - because it was set before the
"install_packages_from_branch_tip" step and - in fact - even before "install database clients" step, which caused our cache to only work for the "base OS dependencies" - installing database clients and installing airflow from branch tip (which works great for CI image) had always been done in PRs because the layers in cache with constraints env invalidated all subsequent layers.

This had no big impact before when testing usually took much longer time - but since the testing has been vastly improved in #35160, now PROD image building continues running even after test complete and becomes the next frontier of optimization.

This PR optimizes PROD image building in two ways:

• caching is prepared with "source_providers" constraint mode, same as regular build

• the AIRFLOW_CONSTRAINT_MODE and related arguments are moved after installing database clients, so that this parameter does not impact their caching.

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[potiuk]

This should likely improve most of PROD building in our CI - PRs that have a need for PROD image to complete, instead of 10-12 minutes waiting for PROD image, will likely have them in 4-5 minutes in most cases.

[potiuk]

Let's see what will be speed improvement with that one (we will only see after cache from that one will be built in main)