When a mod reads as "workshop-xxxxxxx"; it means that the mod is no longer compatible with the current version of DST; or the mod file has become corrupt (which can happen even if others use the same mod without issue).

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You're going to need manually remove the mods from your game files (this happens quite often).

This is an easy fix!:

-Turn off auto-subscribe, if you have it on.

-Unsubscribe from ALL mods, that are showing "workshop-xxxxxxx" for you, on the Steam Workshop page.

-Go into your "Don't Starve Together" file/folder and manually delete ALL of those mods.

To do so; manually delete ALL:

workshop-<number> directories from your
C:\Program Files (x86)\Steam\SteamApps\common\Don't Starve Together\mods directory.

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You can then begin the process of adding those mods back in, one at a time, until you find the one(s) causing the issue.

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Some mod creators update their mods almost immediately after updates/patch fixes/etc, some within weeks/months, others not at all (and those mods become unstable and possibly unusable to the point they can make DST unplayable and game files become corrupt and need to be manually removed).

If you find out the mod(s) causing the issue, you can always leave a comment on that mods Workshop page.

If the creator of the mod(s) causing the issues don't update them.. then there's nothing that you can do to "fix" it. You'll just need to disable whichever mods you find that are causing the issue, and check back in on their Workshop page, every now and again, to see if they've been updated.