drupal_bootstrap() misses some phases in rare cases (Remove $new_phase argument and $final_phase variable from drupal_bootstrap())

If we call drupal_bootstrap() with $new_phase = FALSE, it will not perform phases which are higher than initially requested phase.

Example:

Step 1. We call drupal_bootstrap(DRUPAL_BOOTSTRAP_PAGE_CACHE). We expect that Drupal will return cached page (if configured and cached version is available).

Step 2. drupal_bootstrap() calls _drupal_bootstrap_page_cache(), which (if there are no cache settings in settings.php) calls drupal_bootstrap(DRUPAL_BOOTSTRAP_VARIABLES, FALSE).

Step 3. drupal_bootstrap(), when called with $new_phase = FALSE, ignores all steps which are greater than $final_phase, but $final_phase is DRUPAL_BOOTSTRAP_PAGE_CACHE (and it changes only when $new_phase = TRUE.

if ($new_phase && $phase >= $stored_phase) {
    $final_phase = $phase;
}
...
while ($phases && $phase > $stored_phase && $final_phase > $stored_phase) {
...
}

Step 4. drupal_bootstrap() returns with DRUPAL_BOOTSTRAP_PAGE_CACHE result (instead of expected DRUPAL_BOOTSTRAP_VARIABLES).

Step 5. _drupal_bootstrap_page_cache() tries to read cache settings from db with $cache_enabled = variable_get('cache') and receives FALSE always, since variables have not been loaded.

Result: drupal_bootstrap(DRUPAL_BOOTSTRAP_PAGE_CACHE) never reads cache settings from db.

drupal_bootstrap(DRUPAL_BOOTSTRAP_FULL) used in index.php works just because $final_phase == DRUPAL_BOOTSTRAP_FULL inside drupal_bootstrap() and any requested (with $new_phase = FALSE) phase is performed.

We could remove $new_phase argument and $final_phase variable from drupal_bootstrap() as it was suggested by @chx and @catch 10 years ago (see original issue summary).
I did not find any consequences of removing $new_phase argument.

Documentation should be changed to reflect the changes.

Perhaps, we should implement some testing for drupal_bootstrap() (but I am not sure we really need it).