After core upgraded from Drupal 9.5.11 to Drupal 10.1.1,site gone down

My composer.json files go here....

{
"name": "drupal/recommended-project",
"description": "Project template for Drupal projects with a relocated document root",
"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": {
"aws/aws-sdk-php": "^3.297",
"composer/installers": "^2.2",
"drupal/admin_toolbar": "^3.4",
"drupal/asset_injector": "^2.19",
"drupal/autologout": "^1.4",
"drupal/backup_migrate": "*",
"drupal/bartik": "^1.0",
"drupal/better_exposed_filters": "^6.0",
"drupal/bootstrap": "^3.29",
"drupal/bootstrap_barrio": "^5.5",
"drupal/captcha": "^2.0",
"drupal/chosen": "^4.0",
"drupal/config_filter": "^2.6",
"drupal/config_ignore": "^3.2",
"drupal/config_split": "^2.0",
"drupal/content_access": "^2.0",
"drupal/core-composer-scaffold": "^10.1",
"drupal/core-project-message": "^10.1",
"drupal/core-recommended": "^10.1",
"drupal/csp": "^1.22",
"drupal/csv_serialization": "^4.0",
"drupal/ctools": "^4.0",
"drupal/default_content": "^2.0@alpha",
"drupal/devel": "^5.1",
"drupal/devel_kint_extras": "^1.1",
"drupal/field_group": "^3.4",
"drupal/field_permissions": "^1.3",
"drupal/fontyourface": "^4.0",
"drupal/jquery_ui_slider": "^2.0",
"drupal/lang_dropdown": "^2.1",
"drupal/menu_link_attributes": "^1.3",
"drupal/menu_link_modal": "^2.1",
"drupal/menu_per_role": "^1.5",
"drupal/redirect": "^1.9",
"drupal/redirect_after_login": "^3.0",
"drupal/remove_http_headers": "^2.1",
"drupal/search_api": "^1.31",
"drupal/simplesamlphp_auth": "^4.0",
"drupal/smtp": "^1.2",
"drupal/swagger_ui_formatter": "^4.0",
"drupal/token": "^1.13",
"drupal/twig_tweak": "^3.2",
"drupal/upgrade_status": "^4.0",
"drupal/views_autocomplete_filters": "^2.0",
"drupal/views_bootstrap": "^5.4",
"drupal/views_data_export": "^1.4",
"drupal/viewsreference": "^2.0@beta",
"drush/drush": "^12.4",
"mnsami/composer-custom-directory-installer": "^2.0",
"oomphinc/composer-installers-extender": "^2.0"
},
"conflict": {
"drupal/drupal": "*"
},
"minimum-stability": "stable",
"prefer-stable": true,
"config": {
"allow-plugins": {
"composer/installers": true,
"drupal/core-composer-scaffold": true,
"drupal/core-project-message": true,
"phpstan/extension-installer": true,
"dealerdirect/phpcodesniffer-composer-installer": true,
"cweagans/composer-patches": true,
"oomphinc/composer-installers-extender": true,
"simplesamlphp/composer-module-installer": true,
"mnsami/composer-custom-directory-installer": true
},
"sort-packages": true
},
"extra": {
"drupal-scaffold": {
"locations": {
"web-root": "web/"
}
},
"installer-paths": {
"web/core": [
"type:drupal-core"
],
"web/libraries/{$name}": [
"type:drupal-library"
],
"web/modules/contrib/{$name}": [
"type:drupal-module"
],
"web/profiles/contrib/{$name}": [
"type:drupal-profile"
],
"web/themes/contrib/{$name}": [
"type:drupal-theme"
],
"drush/Commands/contrib/{$name}": [
"type:drupal-drush"
],
"web/modules/custom/{$name}": [
"type:drupal-custom-module"
],
"web/profiles/custom/{$name}": [
"type:drupal-custom-profile"
],
"web/themes/custom/{$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/recommended-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": {
"cweagans/composer-patches": "^1.7"
}
}

“You have requested a non-existent service "theme.manager”.

Some code in that site is not compatible with Drupal 10. Did you follow the official upgrade guide? It includes instructions for checking compatibility.

Yes, I did follow the drupal 9 to 10 official upgrade guide. Installed upgrade status module and fixed contrib module Incompatibility as per the upgrade status module instruction. though I fixed contrib compatibility issue, there was some unexpected compatibility issues while I ran the composer update.

Can you confirm you rebuild the container with drush cr or by running update.php?

You should search the codebase for "theme.manager" as the problematic code will contain that string.