Update core 10.0.x to 10.1.x not possible

That is correct. LinkIt has no full releases that are compatible with Drupal 10 → . You could install a release candidate version, like composer require 'drupal/linkit:^6.0@RC'.

This is not a bug in Drupal Core.

I am moving this to LinkIt's issue queue in case you have other questions.

Perhaps it is a problem in composer.
If I want to install Drupal core 10.1.x the installation failed with the remark that I need an other version of Linkit.
If I want to install Linkit the installation failed with the remark I need an other version of drupal core.
It looks like that both have to be installed at the same time.
The command "--with-all-dependencies" don´t help.

This is not a bug in Composer.

As with all things Composer if you need support it is essential to share the composer.json file here as community members can reproduce your problem and advise.

And also, share the commands you type and the output in detail.

I´ve tried all recommended update commands on the sites of Drupal Core and LINKIT.
The code of composer.json follow here:

{
"name": "drupal/legacy-project",
"description": "Project template for Drupal projects with composer following drupal/drupal layout",
"type": "project",
"license": "GPL-2.0-or-later",
"homepage": " https://www.drupal.org/project/drupal → ",
"support": {
"docs": " https://www.drupal.org/docs/user_guide/en/index.html → ",
"chat": " https://www.drupal.org/node/314178 → "
},
"repositories": [
{
"type": "composer",
"url": "https://packages.drupal.org/8"
}
],
"require": {
"composer/installers": "^2.0",
"drupal/admin_toolbar": "^3.3",
"drupal/asset_injector": "^2.16",
"drupal/backup_migrate": "^5.0",
"drupal/ckeditor_accordion": "^2.0",
"drupal/ckeditor_font": "^2.0@beta",
"drupal/core-composer-scaffold": "^10.0",
"drupal/core-project-message": "^10.0",
"drupal/core-recommended": "^10.0",
"drupal/core-vendor-hardening": "^10.0",
"drupal/ctools": "^4.0",
"drupal/ebt_accordion": "^1.4",
"drupal/ebt_core": "^1.4",
"drupal/ebt_image": "^1.4",
"drupal/ebt_text": "^1.4",
"drupal/editor_advanced_link": "^2.1",
"drupal/fontawesome": "^2.25",
"drupal/honeypot": "^2.1",
"drupal/imce": "^3.0",
"drupal/lang_dropdown": "^2.0",
"drupal/languageicons": "^2.0@beta",
"drupal/layout_builder_modal": "^1.2",
"drupal/layout_builder_styles": "^2.0",
"drupal/linkit": "^6.0@RC",
"drupal/media_library_form_element": "^2.0",
"drupal/pathauto": "^1.11",
"drupal/section_library": "^1.1",
"drupal/svg_image": "^3.0",
"drupal/token": "^1.11",
"drupal/webform": "^6.2@beta",
"wikimedia/composer-merge-plugin": "*"
},
"conflict": {
"drupal/drupal": "*"
},
"minimum-stability": "dev",
"prefer-stable": true,
"config": {
"allow-plugins": {
"composer/installers": true,
"drupal/core-composer-scaffold": true,
"drupal/core-project-message": true,
"drupal/core-vendor-hardening": true,
"phpstan/extension-installer": true,
"dealerdirect/phpcodesniffer-composer-installer": true,
"wikimedia/composer-merge-plugin": true
},
"sort-packages": true
},
"extra": {
"merge-plugin": {
"include": [
"humanity10.org/modules/contrib/webform/composer.libraries.json"
]
},
"drupal-scaffold": {
"locations": {
"web-root": "./"
}
},
"installer-paths": {
"core": [
"type:drupal-core"
],
"libraries/{$name}": [
"type:drupal-library"
],
"modules/contrib/{$name}": [
"type:drupal-module"
],
"profiles/contrib/{$name}": [
"type:drupal-profile"
],
"themes/contrib/{$name}": [
"type:drupal-theme"
],
"drush/Commands/contrib/{$name}": [
"type:drupal-drush"
],
"modules/custom/{$name}": [
"type:drupal-custom-module"
],
"profiles/custom/{$name}": [
"type:drupal-custom-profile"
],
"themes/custom/{$name}": [
"type:drupal-custom-theme"
]
},
"drupal-core-project-message": {
"include-keys": [
"homepage",
"support"
],
"post-create-project-cmd-message": [
" ",
" Congratulations, you’ve installed the Drupal codebase ",
" from the drupal/legacy-project template! ",
" ",
"",
"Next steps:",
" * Install the site: https://www.drupal.org/docs/installing-drupal → ",
" * Read the user guide: https://www.drupal.org/docs/user_guide/en/index.html → ",
" * Get support: https://www.drupal.org/support → ",
" * Get involved with the Drupal community:",
" https://www.drupal.org/getting-involved → ",
" * Remove the plugin that prints this message:",
" composer remove drupal/core-project-message"
]
}
},
"require-dev": {
"drush/drush": "*"
}
}

FWIW, I don't believe the problem you're experiencing with the composer.json file above has to do with Linkit. A minimized version that includes Drupal core and Linkit, as shown below, works:

{
	"repositories": [{
		"type": "composer",
		"url": "https://packages.drupal.org/8"
	}],
	"require": {
		"composer/installers": "^2.0",
		"drupal/core-composer-scaffold": "^10.0",
		"drupal/core-project-message": "^10.0",
		"drupal/core-recommended": "^10.0",
		"drupal/core-vendor-hardening": "^10.0",
		"drupal/linkit": "^6.0@RC"
	},
	"conflict": {
		"drupal/drupal": "*"
	},
	"minimum-stability": "dev",
	"prefer-stable": true,
	"config": {
		"allow-plugins": {
			"composer/installers": true,
			"drupal/core-composer-scaffold": true,
			"drupal/core-project-message": true,
			"drupal/core-vendor-hardening": true
		}
	}
}

As an FYI, we will be providing a stable release of Linkit shortly, so other issues with Composer, such as requiring a minimum stability of dev, should be mitigated.

Great :-) Thank you very much for all your comments and support.