A Sqlite database is only one file, which you surely have access to.
So just add a Database configuration to your IDE and point it to the Sqlite file.
Click on the Database flyout on the left side then on the + (Plus) and add a Sqlite configuration.
(IntelliJ has good documentation on Sqlite Database connection as well of course)

Then you are ready to go.
The UI of the database structure is quite good.
You can browse the tables by doublelick on the table in the database structure view.
Also you can edit values in the table view.
Note: When the DB was created inside the Docker container you probably dont own the DB from the host and you wont be able write to it.
While developing just change permissions on the host, if necessary.

You can also open a Database Console window where you can test queries.
This is particular better than using Adminer because these test queries are persisted and will still be there the next day.
You can add multiple database consoles and reopen them from “Scratches and Consoles” in your Project menu.

So no Adminer needed. Sqlite is just a file, dude.
No hassles with docker-compose anymore for DB administration and still using Docker for the app. :)

Update 09.08.2023:
JetBrains has now also uploaded a nice Youtube Video Tutorial on how to deal with Sqlite databases in IntelliJ IDEs like f.e. PHPStorm:
Working with SQLite Databases in any JetBrains IDE

I learned that you can now Drag and Drop Sqlite database files into the DataBase Pane and the IDE connects it directly, nice!

One thing i usually do on symfony projects in PHPStorm is to edit the “Directories” in the settings to avoid having results from var/cache or var/logs in the search results.

Also it slows down the search which i heavily use. So i exlude all folders that should not be searched because they are cache files or are redundant in some other way.

See this SO post for further discussion: https://stackoverflow.com/questions/35654320/how-to-configure-directories-when-using-a-symfony-project-in-phpstorm

But in IntelliJ Ultimate its a bit different and it took me a bit to figure out.
Here the equivalent is located under “Project Structure->Modules”.
Here you can exclude Directories, set “test” and “source” folders.

Also it seems settings are imported from PHPStorm settings already when using a former PHPStorm project in IntelliJ Ultimate. Nice :)