I'm not a 100% sure that Elgg 3.3 is compatible with Composer v2, but it is with Composer v1. Therefor I'll try to make the steps for for using Composer v1.

What i see already has happened:

• updated PHP to v7.1, however if you wish to use Elgg 3.3 (the latest supported version of Elgg 3) you need PHP 7.2+ but not PHP 8.0 so 7.2, 7.3 or 7.4
• The .htaccess has been updated, for the latest best example check out https://github.com/Elgg/Elgg/blob/3.3/install/config/htaccess.dist

Always make a backup before proceeding with the steps below

The reason some of the composer dependencies couldn't be found is probably that some parts in the composer.json are missing. For the best example check out https://github.com/Elgg/starter-project/blob/3.3/composer.json this is the composer.json which we use to create the ZIP releases here on the community.

When updating the composer.json to the given example please consider directly changing https://github.com/Elgg/starter-project/blob/3.3/composer.json#L9 from "3.*" to "~3.3.0"

After that the following commands can be executed

• "composer update --dry-run" (this will check if there are any issues when updating without actually doing the update)
• if no errors are found run "composer update"
• run "vendor/bin/elgg-cli upgrade async -v" this will execute all database migrations

Your site is now running Elgg 3.3 and can be used again.

The documentation you used was created for updating from Elgg 2.3 to Elgg 3.0 and hasn't been updated after that (for Elgg 3.1 etc). We'll look into that.

I hope this will help somewhat.