The only luggage lockers I could find in Singapore Changi Airport (SIN) are currently not 24/7 (reduced hours or closed due to COVID-19). What's the closest 24/7 luggage locker from Singapore Changi Airport (SIN) (either in or around SIN)?
As far as I can tell you are correct: as of June 2022 there is no 24/7 storage at Changi Airport.
Radical Storage, which leverages hotels to store bags, offers a few 24/7 locations in Singapore but the closest seems to be in Geylang, not very near at all (and not the nicest neighborhood in Singapore at that, it's a red light district).
If you have an early morning flight, one option to avoid hauling around your bag might be early check-in: airlines will typically accept luggage check-ins up to a day in advance. There's a dedicated early check in facility at Jewel, although the hours and airlines available also seem to have been nerfed by COVID, but you can check with your airline for early check-in options at the regular counters as well.
All terminals and Jewel have luggage storage, all of which are 24 hours, except T1. T3 and T4 have them both airside and in the public area. Not really sure about T2, although I passed through it twice last week.
Your best bet as of late 2023 would be Jewel, near the Early Check-In Lounge, or T3, near the train to the city.