Can't run DB upgrades - permission error

[kenahoo]

I originally asked this as a question at Stack Overflow: https://civicrm.stackexchange.com/questions/48137/upgrade-5-66-0-5-66-2-fails-with-permission-error .

I'm using CiviCRM with Wordpress 6.5.3 and MySQL 5.7.44.

I'm attempting to upgrade my CiviCRM from 5.66.0 to 5.66.2. When I get to the DB upgrade stage, when I hit /wp-admin/admin.php?page=CiviCRM&q=civicrm/upgrade&reset=1 -> Upgrade Now -> OK, I just see an empty progress bar and the message [Executed: undefined].

If I switch to the command-line cv (version v0.3.48), and turn on maximum debugging output, I see this:

singersin@s483:~/www/wp$ cv upgrade:db -vvv

Box Requirements Checker
========================

> Using PHP 8.1.28
> PHP is using the following php.ini file:
  /home/singersin/www/wp/php.ini

> Checking Box requirements:
  ✔ The application requires a version matching ">=7.3.0".
  ✔ The application requires the extension "json".
  ✔ The package "psy/psysh" requires the extension "json".
  ✔ The package "nikic/php-parser" requires the extension "tokenizer".
  ✔ The package "psy/psysh" requires the extension "tokenizer".
  
                                                                                                                                                                                                                      
 [OK] Your system is ready to run the application.                                                                                                                                                                    
                                                                                                                                                                                                                      

[BootTrait:debug] Start
[BootTrait:debug] Attempting to set verbose error reporting
[BootTrait:debug] Call standard cv bootstrap
[Bootstrap:debug] Options: {
    "dynamicSettingsFile": "phar:///home/singersin/private/bin/cv/lib/settings_location.php",
    "env": "CIVICRM_SETTINGS",
    "prefetch": true,
    "settingsFile": null,
    "search": true,
    "cmsType": null,
    "httpHost": "",
    "output": {}
}
[Bootstrap:debug] Find settings file
[Bootstrap:debug] Load supplemental configuration for "/home/singersin/www/wp/wp-content/uploads/civicrm/civicrm.settings.php"
[Bootstrap:notice] Find CMS root for "/home/singersin/www/wp"
[Bootstrap:notice] Found "wp" in "/home/singersin/www/wp"
[Bootstrap:notice] Simulate web environment in CLI
[Bootstrap:debug] Load settings file "/home/singersin/www/wp/wp-content/uploads/civicrm/civicrm.settings.php"
[Bootstrap:notice] Initialize class loader
[Bootstrap:notice] Call core bootstrap
[Bootstrap:debug] Finished
[BootTrait:debug] Call core bootstrap
[BootTrait:debug] Call CMS bootstrap
[BootTrait:debug] Set active MySQL timezone
[BootTrait:debug] Finished
[PHP Warning] mkdir(): Permission denied at phar:///home/singersin/private/bin/cv/src/Command/UpgradeDbCommand.php:137

In UpgradeDbCommand.php line 138:
                                                                         
  [RuntimeException]                                                     
  Failed to initialize upgrade data folder: /home/singersin/.cv/upgrade  
                                                                         

Exception trace:
  at phar:///home/singersin/private/bin/cv/src/Command/UpgradeDbCommand.php:138
 Civi\Cv\Command\UpgradeDbCommand->getUpgradeFile() at phar:///home/singersin/private/bin/cv/src/Command/UpgradeDbCommand.php:47
 Civi\Cv\Command\UpgradeDbCommand->execute() at phar:///home/singersin/private/bin/cv/vendor/symfony/console/Command/Command.php:127
 Cvphar\Symfony\Component\Console\Command\Command->run() at phar:///home/singersin/private/bin/cv/vendor/symfony/console/Application.php:637
 Cvphar\Symfony\Component\Console\Application->doRunCommand() at phar:///home/singersin/private/bin/cv/vendor/symfony/console/Application.php:190
 Cvphar\Symfony\Component\Console\Application->doRun() at phar:///home/singersin/private/bin/cv/src/Application.php:67
 Civi\Cv\Application->doRun() at phar:///home/singersin/private/bin/cv/vendor/symfony/console/Application.php:101
 Cvphar\Symfony\Component\Console\Application->run() at phar:///home/singersin/private/bin/cv/src/Application.php:33
 Civi\Cv\Application::main() at phar:///home/singersin/private/bin/cv/bin/cv:28
 require() at /home/singersin/private/bin/cv:14

I'm assuming this is because I don't have permission to create directories in $HOME (the site's hosting provider doesn't allow it):

$ ls -ld ~
drwxr-x---+ 15 root singersin 4096 Mar  9  2020 /home/singersin

Can I specify a different temporary directory for it to perform its work somehow? Trying HOME=$HOME/private/tmp cv upgrade:db didn't work, it still tried to create .cv/upgrade in the original non-writeable location. This seems to be because PHP in general doesn't allow overriding HOME:

$ HOME=foo BAR=baz php -r '$home=getenv("HOME"); $bar=getenv("BAR"); echo("[$home;$bar]\n");'
[/home/singersin;baz]

CGI binaries will let me override HOME, but cv refuses to run from a CGI binary:

$ HOME=$HOME/private/tmp php81.cgi bin/cv
Content-type: text/html


The application may only be invoked from a command line, got "cgi-fcgi"

I'm also wondering if there's some place I can find the DB update steps and just run them manually, is that an option? How can I find those SQL statements?