Yes, you can directly upgrade your Odoo database from version 15 to version 19, even with custom modules. You don't need to upgrade incrementally through each version.

However, upgrading a database with custom modules requires extra steps:

Stop development: Freeze the codebase to avoid having to re-upgrade and re-test features.

Request an upgraded test database: This allows you to test the upgrade process without affecting your live data. You can request multiple test databases if needed.

Make your modules installable on an empty database: Ensure your custom modules are compatible with the new Odoo version by installing them on an empty database and resolving any errors or warnings.

Make your modules installable on the upgraded database: Migrate data and test the modules to ensure they work correctly with the upgraded database.

Test extensively and do a rehearsal: Thoroughly test the upgraded database and perform a rehearsal to identify and fix any issues before upgrading the production database.

With Odoo Enterprise, upgrading to the latest version is free, including support to resolve potential issues.Please refer the Upgrade docs

https://www.odoo.com/documentation/19.0/developer/howtos/upgrade_custom_db.html

@Odoo consultant, are you making things up? Have you ever done an upgrade? Or are you just posting bullshit from an AI?
Wish i could downvote your comment...
As @Ray Carnes (ray) said, the databse needs to be updated from one version to the following one, so from 17 to 18, and later from 18 to 19 (you can run them one after the other, but the migration is a one step version upgrade)
Your modules could be upgraded to the 19th version, but then how will you test nothing is broken in the 18th version? You can't, so its up to you.