Permission to Kernel

Your software
My PHP version is : 7.4
*My MySQL version is: 7.4.33

Updating/Installing Errors
*I am: Installing
*installing via: Command Line

These errors are showing in the installer :
composer install
PHP Warning: PHP Startup: Unable to load dynamic library ‘soap’ (tried: /usr/lib/php/20190902/soap (/usr/lib/php/20190902/soap: cannot open shared object file: No such file or directory), /usr/lib/php/20190902/soap.so (/usr/lib/php/20190902/soap.so: cannot open shared object file: No such file or directory)) in Unknown on line 0

Warning: PHP Startup: Unable to load dynamic library ‘soap’ (tried: /usr/lib/php/20190902/soap (/usr/lib/php/20190902/soap: cannot open shared object file: No such file or directory), /usr/lib/php/20190902/soap.so (/usr/lib/php/20190902/soap.so: cannot open shared object file: No such file or directory)) in Unknown on line 0
Installing dependencies from lock file (including require-dev)
Verifying lock file contents can be installed on current platform.
Your lock file does not contain a compatible set of packages. Please run composer update.

Problem 1
- bandwidth-throttle/token-bucket is locked to version 2.0.0 and an update of this package was not requested.
- bandwidth-throttle/token-bucket 2.0.0 requires ext-bcmath * → it is missing from your system. Install or enable PHP’s bcmath extension.
Problem 2
- mautic/core-lib is locked to version 4.3.x-dev and an update of this package was not requested.
- mautic/core-lib 4.3.x-dev requires ext-zip * → it is missing from your system. Install or enable PHP’s zip extension.
Problem 3
- phpoffice/phpspreadsheet is locked to version 1.23.0 and an update of this package was not requested.
- phpoffice/phpspreadsheet 1.23.0 requires ext-zip * → it is missing from your system. Install or enable PHP’s zip extension.

These errors are showing in the Mautic log :
Nothing

Your problem
My problem is :
Warning: require(/mautic/vendor/composer/…/…/app/AppKernel.php): failed to open stream: Permission denied in /mautic/vendor/composer/autoload_real.php on line 78

Fatal error: require(): Failed opening required /mautic/vendor/composer/…/…/app/AppKernel.php’ (include_path=‘.:/usr/share/php’) in /mautic/vendor/composer/autoload_real.php on line 78

Steps I have tried to fix the problem :
Problems during installation I solved by composer install --ignore-platform-req=ext-bcmath --ignore-platform-req=ext-zip

Looks like you are missing the soap PHP extension.

ref:
Unable to load dynamic library ‘soap’