Here's a solution using a function I found from php documentation:
<?php
/*
Question Author: Not a Pro
Question Answerer: Jacob Mulquin
Question: Sort Nested Array base on Value in PHP
URL: https://stackoverflow.com/questions/76419733/sort-nested-array-base-on-value-in-php
Tags: php, arrays
*/
// Author: jimpoz at jimpoz dot com
// URL: https://www.php.net/manual/en/function.array-multisort.php#100534
function array_orderby()
{
    $args = func_get_args();
    $data = array_shift($args);
    foreach ($args as $n => $field) {
        if (is_string($field)) {
            $tmp = array();
            foreach ($data as $key => $row)
                $tmp[$key] = $row[$field];
            $args[$n] = $tmp;
            }
    }
    $args[] = &$data;
    call_user_func_array('array_multisort', $args);
    return array_pop($args);
}
function sortProjectsByClientName(&$projects)
{
    foreach ($projects as &$project) {
        $project['Client'] = array_orderby($project['Client'], 'Name', SORT_ASC);
    }
}
$projects = [
    [
        'project_id' => 1,
        'Client' => [
            ['Name' => 'Franco',
            'Amount' => 1000.00,
             ],
             ['Name' => 'Allan',
            'Amount' => 1000.00,
            ],
            ['Name' => 'Booby',
            'Amount' => 1000.00,
            ]
        ],
      
    ],
    [
        'project_id' => 2,
        'Client' => [
            ['Name' => 'Bob',
            'Amount' => 1000.00,
             ],
             ['Name' => 'Trevor',
            'Amount' => 1000.00,
            ],
            ['Name' => 'Alice',
            'Amount' => 1000.00,
            ]
        ],
      
    ]
];
sortProjectsByClientName($projects);
var_dump($projects);
Yields:
array(2) {
  [0]=>
  array(2) {
    ["project_id"]=>
    int(1)
    ["Client"]=>
    array(3) {
      [0]=>
      array(2) {
        ["Name"]=>
        string(5) "Allan"
        ["Amount"]=>
        float(1000)
      }
      [1]=>
      array(2) {
        ["Name"]=>
        string(5) "Booby"
        ["Amount"]=>
        float(1000)
      }
      [2]=>
      array(2) {
        ["Name"]=>
        string(6) "Franco"
        ["Amount"]=>
        float(1000)
      }
    }
  }
  [1]=>
  array(2) {
    ["project_id"]=>
    int(2)
    ["Client"]=>
    array(3) {
      [0]=>
      array(2) {
        ["Name"]=>
        string(5) "Alice"
        ["Amount"]=>
        float(1000)
      }
      [1]=>
      array(2) {
        ["Name"]=>
        string(3) "Bob"
        ["Amount"]=>
        float(1000)
      }
      [2]=>
      array(2) {
        ["Name"]=>
        string(6) "Trevor"
        ["Amount"]=>
        float(1000)
      }
    }
  }
}