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Converting a TIFF (or other standard image type) to a DNG file won't create a raw capture, even though DNG can be used as a raw capture format. In other words, you won't be getting the advantages of a raw capture by using this workflow. In addition, the DNG file would not contain the layers you created for the TIFF image in Photoshop. Therefore, the only real benefit would be that the DNG file would have a smaller file size compared to the TIFF image.
I strongly recommend retaining the edited file with all layers as a master image to be used for the basis of all output for sharing the image later. In this context it wouldn't make sense to convert the TIFF file to DNG.
If you did want to convert an image file to a DNG, this can be done very easily in Lightroom Classic or Lightroom using the Export feature. In both applications this command can be found on the menu at File > Export, and as part of the export process you can choose to export as a DNG image. This would enable you to batch export multiple images, by the way.
It is also possible to open a TIFF image in Camera Raw by opening the TIFF image via Adobe Bridge. However, Camera Raw only supports flattened TIFF images, so you would need to flatten the image to use this workflow, which again I don't recommend. But if you did open a TIFF (or raw or JPEG) image in Camera Raw, you can click on the "more" button (the three dots) on the thumbnail for the image after enabling the filmstrip view. There you'll find the Save Image > Save Image command (or presets for saved settings) where you can process the image into a DNG file.
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