You can go to the Preferences for Camera Raw by going to the Edit menu (For Windows) and the Photoshop Menu (For Mac), then navigate to Preferences > Camera Raw, then select File Handling and change the settings for TIFF and JPEG (if required) to Automatically open all supported JPEG/TIFF from the drop down. Then click OK, quit and relaunch Photoshop.
I found those settings already as you describe. Did not fix the problem. I typically edit my dngs in ACR, then move to PS and save finished work as a tiff. Its some my edited tiffs that don’t get the option to open in ACR. I have not been able to find any reason for the seemingly random failure of some edited tiffs to open. I also notice edited photos saved as .psd never seem to open in ACR. This is a phenomenon that started happening recently, after years of no such problems.
PSD files can not be opened with Camera raw, this has never been possible. For the TIFF files you are facing issues with, how ever those files saved and do you have multiple layers in the files? You would be able to open TIFF files in Camera Raw that have a single layer.