Dependency conflict with Magento 2.4.4

Unable to install the prerelease of Magento 2.4.4 while the Data Migration Tool is installed due to conflicting Monolog packages.

A similar issue has been raised in the magento/magento2 repository, though I believe this will have to be fixed here.

Preconditions (*)

1. Magento 2.4.3 installed
2. magento/data-migration-tool (latest, 2.4.3) installed
3. composer access to prerelease of 2.4.4

Steps to reproduce (*)

1. composer require-commerce magento/product-community-edition 2.4.4 --no-update --interactive-root-conflicts
2. composer update

Expected result (*)

1. Dependencies should resolve and Magento 2.4.4 and its dependencies should be installed.

Actual result (*)

  Problem 1
    - Root composer.json requires magento/data-migration-tool ^2.4 -> satisfiable by magento/data-migration-tool[2.4.0, 2.4.1, 2.4.2, 2.4.3].
    - magento/product-community-edition 2.4.4 requires monolog/monolog ^2.3 -> satisfiable by monolog/monolog[2.3.0, ..., 2.4.0].
    - You can only install one version of a package, so only one of these can be installed: monolog/monolog[1.0.0, ..., 1.27.0, 2.0.0, ..., 2.4.0].
    - magento/product-enterprise-edition 2.4.4 requires magento/product-community-edition 2.4.4 -> satisfiable by magento/product-community-edition[2.4.4].
    - magento/data-migration-tool[2.4.0, ..., 2.4.3] require monolog/monolog ^1.17 -> satisfiable by monolog/monolog[1.17.0, ..., 1.27.0].
    - Root composer.json requires magento/product-enterprise-edition 2.4.4 -> satisfiable by magento/product-enterprise-edition[2.4.4].

References

1. First, upgrade process for above was obtained from the Adobe doc here.
2. This was caused in this Pull Request, while this Issue was being addressed.
3. To resolve, data-migration-tool will need to update to Monolog ^2. A Monolog-written guide on that can be found here.

Start with the root composer.json and the reported composer require and update commands, then read the linked Monolog UPGRADE guide to understand the required dependency change. Reproduce the conflict with Magento 2.4.4 and confirm the data-migration-tool dependencies resolve with Monolog 2 without breaking the migration tool.