Cannot install Entity Clone 2.0.0 because this module requires ^1.0 in composer.json

I am having the same issue.

Attached a patch

You can hack around this by doing this in composer.json:
"drupal/entity_clone": "2.0.0-beta4 as 1.0"

It would be great to have this committed though, this is quite a nasty workaround.

Successfully applying the patch provided in #4 didn't solved the issue on my side

composer install
Gathering patches for root package.
Removing package drupal/menu_link_clone so that it can be re-installed and re-patched.
  - Removing drupal/menu_link_clone (3.2.0)
Deleting web/modules/contrib/menu_link_clone - deleted
> DrupalProject\composer\ScriptHandler::checkComposerVersion
Installing dependencies from lock file (including require-dev)
Verifying lock file contents can be installed on current platform.
Warning: The lock file is not up to date with the latest changes in composer.json. You may be getting outdated dependencies. It is recommended that you run `composer update` or `composer update <package name>`.
Package operations: 1 install, 0 updates, 0 removals
Gathering patches for root package.
Gathering patches for dependencies. This might take a minute.
  - Installing drupal/menu_link_clone (3.2.0): Extracting archive
  - Applying patches for drupal/menu_link_clone
    https://www.drupal.org/files/issues/2023-08-09/menu_link_clone_3365946-4.patch (Cannot install Entity Clone 2.0.0)
Generating autoload files
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Use the `composer fund` command to find out more!
> DrupalProject\composer\ScriptHandler::createRequiredFiles

composer require 'drupal/entity_clone:^2.0@beta'
./composer.json has been updated
Running composer update drupal/entity_clone
Gathering patches for root package.
> DrupalProject\composer\ScriptHandler::checkComposerVersion
Loading composer repositories with package information
Updating dependencies
Your requirements could not be resolved to an installable set of packages.

  Problem 1
    - Root composer.json requires drupal/entity_clone ^2.0@beta, found drupal/entity_clone[2.0.0-beta2, 2.0.0-beta3, 2.0.0-beta4] but these were not loaded, likely because it conflicts with another require.
  Problem 2
    - drupal/menu_link_clone is locked to version 3.2.0 and an update of this package was not requested.
    - drupal/menu_link_clone 3.2.0 requires drupal/entity_clone ^1.0 -> found drupal/entity_clone[1.0.0-beta1, ..., 1.0.0-beta7] but it conflicts with your root composer.json require (^2.0@beta).

Use the option --with-all-dependencies (-W) to allow upgrades, downgrades and removals for packages currently locked to specific versions.

Installation failed, reverting ./composer.json and ./composer.lock to their original content.