Usually when you arrive from JFK on SQ25 and are continuing to SIN, they will have SQ ground agents waiting at the end of the jet bridge before entering the terminal, directing transit pax to the secure area. Same for the reverse journey on SQ26 to JFK when arriving from SIN.

Apparently, you can book access to LH lounges from here. Can’t say it works or still possible as I have never tried, but do recall a press release or something similar from LH during covid, advertising the option of purchasing access.