tl;dr - Reconnect your external applications to Capture One by right-clicking on an image and choosing "Edit with..." and then "Other ..." if they are not in the Edit with dropdown list.
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There is no plug in for these applications*. Presumably, you are using the "Edit with ..." operation in Capture One to pass a rendered (RGB, not raw) file to the external application of your choosing (for instance, Nik Color Efex or Topaz Studio). You typically right-click on an image and select "Edit with..." and then choose the external application from the existing dropdown list. If your application has not already been connected to Capture One, you can choose the "Other ..." menu item and navigate to the executable application to link that application to Capture One as a choice for an external editor. When you select the external application of your choice, Capture One will present you with a dialog that permits you to specify the rendered output file type, color space profile and bit depth, etc. and will then render the file and pass the rendered file to the external application that you chose. When you are finished in the external application, the changes will be saved to the rendered file and that rendered file will be updated in Capture One to reflect the changes made in the external application.
Presumably this is the workflow that you are describing, and the workflow that has been interrupted by the update.
Try right-clicking on an image and choosing "Edit with ..." to see if your external applications are still in the dropdown list. If they are, you are good to go. If they are not, then select "Other ..." and relink them to Capture One.
As an aside, Capture One also has a "Open with ..." option - this is different than "Edit with ..." in that "Open with ..." will pass the raw file to the external application of your choice, with no adjustments from Capture One. It literally just passes the raw file to the external application. You may want to do this, for example, if there is an external application that performs a task that you need in your workflow prior to working on the image in Capture One. For example, in Capture One I can right-click on a raw file from my Fujifilm GFX 50s and "Open with ..." DxO PhotoLab to perform noise reduction and optical correction on the file. I can save the result from DxO as a DNG (linear, demosaiced DNG) that I can then edit in Capture One.
*CAVEAT - this is how the workflow is on a Mac. It may be different on a PC, and I do not use PCs so this may all be completely irrelevant, and I apologize in advance.
Kirk