After we upgraded Composer on our development environment, we checked and found our projects only complained about one or two plugins. For some of the sites we needed to update cweagans/composer-patches to version ^1.7.0. For some we needed to update composer/installers to version ^1.9. For the sites we Composerized using the Grasmash composerize-drupal plugin we had to remove the plugin and all the packages that came with it (they are no more needed for the site to work once the site got Composerized).
As simple as these steps and our sites were working with Composer 2. Composer 2 is so much faster and uses far less memory. It's a big relief to remove Composer wait time from our development process not to talk of making sure there is enough high memory for Composer on our machines.
Here are some info from the official release:
We overhauled pretty much everything from the protocol used between Composer and packagist.org to the dependency resolution, including downloading files in parallel using curl and constraint evaluation optimizations. This leads to massive improvements in terms of both speed and memory usage. The difference depends on your use case, so while I've seen reports of improvements of over 50% to both in some projects, I cannot put an exact number on it. But I am sure you will be positively surprised if you haven't tried Composer 2 yet.
As a side note to this,
removeand partial updates are now much faster because Composer will now only load the metadata of the packages which are being changed.