Is this what you're looking for?
Response ID: ${e://Field/ResponseID}

You can also use ${l://SurveySessionID} to get the session ID, but I'd probably stick with the Response ID

Not really the ResponseID, but the Participant Unique ID.
I have a survey flow where the participant needs to input their UniqueID before they can take the survey.
I've uploaded a participant list with a Unique Identifier.
Right now I can't find a piped text where it can show the UniqueID they entered

If the data is saved in a contact list - did you add an element in your survey flow to call and save that embedded data from the contact list? Then try adding the piped text from that embedded data field
Is your UniqueID saved as the ExternalDataReference? I think you typically need to use an email or the ExternalDataReference field for the authenticator to work

The data came from manually adding participants and searching the directory.
Whenever I try to add an embedded data from the survey flow, it's not showing the UniqueID. The UniqueID is saved as the UniqueID in the directory.

Hmm. Are you trying to call what they typed into the authenticator? Or are you trying to call the information that is saved in that directory field?
And you're saying you tried adding an embedded data field called "UniqueID" to your survey flow, but it's not returning any information for participants when you reference

${e://Field/UniqueID}

Calling the one typed in the authenticator, which is similar to the one saved in the participant list.
For the next line of question, I tried adding UniqueID to the survey flow via embedded data but it's not on the list.