Database file at path `/var/www/sites/website.com/database/database.sqlite` does not exist, but running `php artisan migrate` works just fine

Suppose I have a Laravel 11 application running at www.website.com, which is hosted at a linux machine. The application has a poor response time because it has to fetch data from three databases before it can return a response to the user. As such, I thought it would be a good idea to host a SQLite database at www.website.com to cache the results of read-intensive operations so the application can serve the results to the user immediately (I've considered Redis and Memched, but I decided to work with SQLite since I was already familiar with it). The concept worked on my local machine, so I pushed it over to the dev server for further testing before pushing it to the production and started configuring it.

The configuration process had the following steps:

1. I accidentally deleted the database.sqlite file at the database directory before, so I replaced with a fresh database.sqlite and ran chmod 776 on it. This file is stored in the database directory in the default Laravel directory configuration. I'm perfectly aware that permissions this open is a bad idea, but since this is a dev server where things are usually broken during testing its fine. I was planning to change its permissions before pushing it to production.
2. I also gave the database directory chmod 776 permissions.
3. The .env was configured accordingly and I set the sqlite's filepath to /var/www/sites/website.com/database/database.sqlite.
4. I ran migrations using php artisan migrate. No issues there. The migration was Laravel's default cache table.

However, trying to open the website failed and threw a 500 Internal Server Error. After checking the logs, it turns out that the app can't find the location of the database/database.sqlite. What made me confused was that the migrations in step 4 worked just fine without issue, so the app could find the location of the database. Furthermore, after checking the config at config/database.php, I found no issues.

Here is the relevant .env file and config/database.php sections of the code respectively. They might be useful in debugging.

.env

DB_CONNECTION=sqlite_cache
DB_DATABASE=/var/www/sites/website.com/database/database.sqlite
CACHE_STORE=database
DB_CACHE_CONNECTION=sqlite_cache
DB_CACHE_TABLE=cache
DB_CACHE_LOCK_CONNECTION=sqlite_cache
DB_CACHE_LOCK_TABLE=cache_locks

config/database.php

'sqlite_cache' => [
'driver' => 'sqlite',
'url' => env('DB_URL'),
'database' => env('DB_DATABASE', database_path('database.sqlite')),
'prefix' => '',
'foreign_key_constraints' => env('DB_FOREIGN_KEYS', true),
'busy_timeout' => null,
'journal_mode' => null,
'synchronous' => null,
],

Right now, what caused the php artisan migrate command to work but not the application? How can I get the application to detect the existence of the database?

What I tried: The steps described above. What I expected to happen: The application runs just fine, since the php artisan migrate commands ran just fine. What actually happened: The application couldn't locate the location of the sqlite database, even though the php artisan migrate and its related commands worked just fine.