Update 8202 will not apply, causing Drupal to think there is always an update pending

Same, the update notification never goes away.

Here is a screenshot of the update page.

I had the same issue until I updated the following additional modules. After updating these additional modules, the dropzonejs_eb_widget update 8202 successfully applied:

media_entity: updated from 8.x-1.7 to 8.x-2.0-beta1
entity_browser: updated from 8.x-1.4 to 8.x-2.0-dev from January 9, 2018

I believe the original poster updated media_entity but did not mention updating entity_browser. I believe that was the missing piece.

I followed the media_entity update procedure listed on the project page, https://www.drupal.org/project/media_entity.

Hope this helps others.

I am running a distro, I am not sure I can do that on my own yet (distro depends on it).

I'm experiencing the same problem but updating entity_browser module did not solve the issue. The media_entity module is not installed on our site at all and it appears that was the issue in our case.
The update hook dependencies for media_entity was causing the problem for us and made the update not run as expected.

Adding an extra check to see if that module exist before using the dependency solves the issue and update are applied clean.
Hope this patch can help someone.

Make sure your media_entity is using 8.2. Update 8202 depends on update 8201 of the media_entity module.

#7 corrects the issue. My site doesn't have media_entity installed.

Ref #5: I updated (with composer.json edits) to entity_browser 2.0.0-alpha2, and media_entity 2.0.0-beta2.
Update 8202 still won't run. What did I miss? Do I need to run patch #7. Any help appreciated here.

If the problem is not fixed by upgrading the modules I would suggest you to try the patch and ping pack with an update after. It will help in the review of this issue. Thanks!

The patch worked for me.

Patch worked for me too!
Composer remove drupal/dropzonejs drupal/dropzonejs_eb_widget
Added to composer.json:

        },
        "patches": {
            "drupal/dropzonejs": {
                "Dropzonejs enable applying 8202 update": "https://www.drupal.org/files/issues/2018-03-09/2935637-7.patch"}     
            }

Ran composer update:

Package operations: 1 install, 0 updates, 0 removals
Gathering patches for root package.
Gathering patches for dependencies. This might take a minute.
  - Installing drupal/dropzonejs (dev-2.x 7af9fd0): Cloning 7af9fd05f8 from cache
  - Applying patches for drupal/dropzonejs
    https://www.drupal.org/files/issues/2018-03-09/2935637-7.patch (Dropzonejs enable applying 8202 update)

Result:

$   composer show drupal/drop*
drupal/dropzonejs           2.x-dev 7af9fd0 Drupal integration for DropzoneJS - An open source library that provi...
drupal/dropzonejs_eb_widget 2.x-dev         DropzoneJS Entity browser widget

I can confirm also that the patch in comment #7 works.

Basically I needed to update the site and just did a `composer update` to update core and contrib.

Core and Related Contrib Modules:

• Drupal 8.3.9 to 8.5.2
• Core: Media - Not Installed
• Media entity (media_entity) from 8.1.6 to 8.1.7 - Not Installed
• Entity Browser (entity_browser) from 8.1.0-rc2 to 8.1.4 - Installed
• dropzonejs (dropzonejs) from 8.1.0-alpha5 - 8.x-2.0-alpha3 - Installed
• DropzoneJS entity browser widget (dropzonejs_eb_widget) at 8.x-2.0-alpha3 - Installed

Patch in #7 works for me too, it requires the db updates to run once and then hides the message.

Moving to RTBC

Trouble applying patch

Re-typed command and it worked. Sorry to bug you all.

Thanks everyone, I committed the patch.