as sbs2716g mentioned, there are travelators from jewel to T3. there are skytrains from T1/Jewel to T3. both are covered indoors
both travelators and skytrain gets to the rightside of terminal 3 (as you can see from this map), and you have to manually walk to the left side of T3
https://www.changiairport.com/en/map.../103.98803/-67
that landside&airside T3 skytrain picks up from the northside of T1 (which is connected to jewel), but its still a decent walk from jewel
https://www.changiairport.com/en/map...103.989389/-67
that landside&airside T3 skytrain also goes through (but does not stop at )Jewel, then picks up at T2. the view is pretty good
https://www.changiairport.com/en/map...103.990038/-67