指摘事項を修正しました。
もし他にありましたらご指摘お願いいたします。

★以下緊急対処手順ができなかった
●サーバーにある削除したいプラグインディレクトリの削除
　→インストールされていないので存在しない
●conposer.jsonから削除したいプラグインの定義を削除
　→定義が見つからない

【最新のインストールエラー】
キャッシュ削除をして以下のエラーが表示されました。


システムエラーが発生しました。

ログを確認
**************** AddShippingCostPerItem42 ****************
<warning>A script named compile would override a Composer command and has been skipped</warning>
<warning>A script named auto-scripts would override a Composer command and has been skipped</warning>
<warning>A script named installer-scripts would override a Composer command and has been skipped</warning>
[6.5MiB/21.29s] ./composer.json has been updated
[7.9MiB/21.33s] Running composer update ec-cube/addshippingcostperitem42 --with-dependencies
[11.0MiB/21.34s] Loading composer repositories with package information
[11.9MiB/46.28s] <warning>Dependency ec-cube/plugin-installer is also a root requirement. Package has not been listed as an update argument, so keeping locked at old version. Use --with-all-dependencies (-W) to include root dependencies.</warning>
[12.2MiB/46.29s] Updating dependencies
[14.0MiB/46.30s] Your requirements could not be resolved to an installable set of packages.
[14.0MiB/46.30s]
Problem 1
- lcobucci/jwt 5.3.0 requires ext-sodium * -> it is missing from your system. Install or enable PHP's sodium extension.
- league/oauth2-server-bundle v0.5.0 requires league/oauth2-server ^8.3 -> satisfiable by league/oauth2-server[8.5.4].
- ec-cube/api42 4.3.1 requires league/oauth2-server-bundle ^0.5 -> satisfiable by league/oauth2-server-bundle[v0.5.0].
- league/oauth2-server 8.5.4 requires lcobucci/jwt ^4.3 || ^5.0 -> satisfiable by lcobucci/jwt[5.3.0].
- ec-cube/api42 is locked to version 4.3.1 and an update of this package was not requested.

To enable extensions, verify that they are enabled in your .ini files:
- /etc/php-fpm/php81-php.ini
- /opt/php-8.1.29/etc/php.d/apcu.ini
- /opt/php-8.1.29/etc/php.d/bcmath.ini
- /opt/php-8.1.29/etc/php.d/dba.ini
- /opt/php-8.1.29/etc/php.d/dom.ini
- /opt/php-8.1.29/etc/php.d/gd.ini
- /opt/php-8.1.29/etc/php.d/imagick.ini
- /opt/php-8.1.29/etc/php.d/imap.ini
- /opt/php-8.1.29/etc/php.d/intl.ini
- /opt/php-8.1.29/etc/php.d/ldap.ini
- /opt/php-8.1.29/etc/php.d/mbstring.ini
- /opt/php-8.1.29/etc/php.d/mcrypt.ini
- /opt/php-8.1.29/etc/php.d/mysqli.ini
- /opt/php-8.1.29/etc/php.d/pdo.ini
- /opt/php-8.1.29/etc/php.d/pdo_mysql.ini
- /opt/php-8.1.29/etc/php.d/pdo_pgsql.ini
- /opt/php-8.1.29/etc/php.d/pdo_sqlite.ini
- /opt/php-8.1.29/etc/php.d/pgsql.ini
- /opt/php-8.1.29/etc/php.d/soap.ini
- /opt/php-8.1.29/etc/php.d/xmlreader.ini
- /opt/php-8.1.29/etc/php.d/xmlwriter.ini
- /opt/php-8.1.29/etc/php.d/xsl.ini
You can also run `php --ini` in a terminal to see which files are used by PHP in CLI mode.
Alternatively, you can run Composer with `--ignore-platform-req=ext-sodium` to temporarily ignore these required extensions.
[14.0MiB/46.30s] <warning>Running update with --no-dev does not mean require-dev is ignored, it just means the packages will not be installed. If dev requirements are blocking the update you have to resolve those problems.</warning>
[12.5MiB/46.30s] You can also try re-running composer require with an explicit version constraint, e.g. "composer require ec-cube/AddShippingCostPerItem42:*" to figure out if any version is installable, or "composer require ec-cube/AddShippingCostPerItem42:^2.1" if you know which you need.
[12.5MiB/46.30s]
Installation failed, reverting ./composer.json and ./composer.lock to their original content.
[12.5MiB/46.30s] Memory usage: 12.48MiB (peak: 14.43MiB), time: 46.3s

{"success":false,"log":"\u003Cwarning\u003EA script named compile would override a Composer command and has been skipped\u003C\/warning\u003E\n\u003Cwarning\u003EA script named auto-scripts would override a Composer command and has been skipped\u003C\/warning\u003E\n\u003Cwarning\u003EA script named installer-scripts would override a Composer command and has been skipped\u003C\/warning\u003E\n[6.5MiB\/21.29s] .\/composer.json has been updated\n[7.9MiB\/21.33s] Running composer update ec-cube\/addshippingcostperitem42 --with-dependencies\n[11.0MiB\/21.34s] Loading composer repositories with package information\n[11.9MiB\/46.28s] \u003Cwarning\u003EDependency ec-cube\/plugin-installer is also a root requirement. Package has not been listed as an update argument, so keeping locked at old version. Use --with-all-dependencies (-W) to include root dependencies.\u003C\/warning\u003E\n[12.2MiB\/46.29s] Updating dependencies\n[14.0MiB\/46.30s] Your requirements could not be resolved to an installable set of packages.\n[14.0MiB\/46.30s] \n Problem 1\n - lcobucci\/jwt 5.3.0 requires ext-sodium * -\u003E it is missing from your system. Install or enable PHP\u0027s sodium extension.\n - league\/oauth2-server-bundle v0.5.0 requires league\/oauth2-server ^8.3 -\u003E satisfiable by league\/oauth2-server[8.5.4].\n - ec-cube\/api42 4.3.1 requires league\/oauth2-server-bundle ^0.5 -\u003E satisfiable by league\/oauth2-server-bundle[v0.5.0].\n - league\/oauth2-server 8.5.4 requires lcobucci\/jwt ^4.3 || ^5.0 -\u003E satisfiable by lcobucci\/jwt[5.3.0].\n - ec-cube\/api42 is locked to version 4.3.1 and an update of this package was not requested.\n\nTo enable extensions, verify that they are enabled in your .ini files:\n - \/etc\/php-fpm\/php81-php.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/apcu.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/bcmath.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/dba.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/dom.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/gd.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/imagick.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/imap.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/intl.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/ldap.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/mbstring.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/mcrypt.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/mysqli.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/pdo.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/pdo_mysql.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/pdo_pgsql.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/pdo_sqlite.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/pgsql.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/soap.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/xmlreader.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/xmlwriter.ini\n - \/opt\/php-8.1.29\/etc\/php.d\/xsl.ini\nYou can also run `php --ini` in a terminal to see which files are used by PHP in CLI mode.\nAlternatively, you can run Composer with `--ignore-platform-req=ext-sodium` to temporarily ignore these required extensions.\n[14.0MiB\/46.30s] \u003Cwarning\u003ERunning update with --no-dev does not mean require-dev is ignored, it just means the packages will not be installed. If dev requirements are blocking the update you have to resolve those problems.\u003C\/warning\u003E\n[12.5MiB\/46.30s] You can also try re-running composer require with an explicit version constraint, e.g. \u0022composer require ec-cube\/AddShippingCostPerItem42:*\u0022 to figure out if any version is installable, or \u0022composer require ec-cube\/AddShippingCostPerItem42:^2.1\u0022 if you know which you need.\n[12.5MiB\/46.30s] \nInstallation failed, reverting .\/composer.json and .\/composer.lock to their original content.\n[12.5MiB\/46.30s] Memory usage: 12.48MiB (peak: 14.43MiB), time: 46.3s\n"}

対応がありましたら教えてください。

と出力されていますので、PHP-sodium 拡張ライブラリがないのでエラーになっています。
PHP-sodium 拡張ライブラリをインストールするか、下記のサイトを参考にしてみてください。
https://doc4.ec-cube.net/quickstart/trouble-shooting-for-plugin-install

----------------
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
EC-CUBEインテグレートパートナー【ゴールド】ランク
M&I Works
URL: https://miworks.biz/
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

返信ありがとうございます。

【回避方法を選択】

アンインストールするプラグインとは＜EC-CUBE Web API プラグイン(4.2/4.3系)＞だと思いますが、インストールされていないのでPluginからディレクトリ削除できません。

※オーナーズストアでは「インストール」表示

PHP-sodium 拡張ライブラリをインストールする以外の方法はありますでしょうか‥

下記サイトの質問用テンプレートに沿って、サーバ環境および現環境を記載してみてください。
https://xoops.ec-cube.net/modules/tinyd0/index.php?id=8

----------------
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
EC-CUBEインテグレートパートナー【ゴールド】ランク
M&I Works
URL: https://miworks.biz/
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>