No. Compression fittings do not need PTFE tape, and many hoses seal with an internal washer. Use sealant only where the fitting’s instructions require it. Threaded appearance alone does not tell you how a joint seals.
Check that both supplies are open, the hoses are not kinked and the manufacturer’s flush procedure was completed. Installation debris can restrict the aerator or spray head. Isolate the supplies before any disassembly that the manual requires.