2000 KM is just a deception range set during JCPOA, it has no meaning. IISS estimated K-4 and Sejjil-II to be ranging 3200-3500 KM with regular <1 tonne warheads. To show their ranges at 2000 KM after JCPOA, IRGCASF started advertising them esp K-4 with ~2000 KG warhead to compensate for JCPOA set 2000 KM barrier. It was a joke among Iranian missile community back then when it happened because same missiles were being shown again with twice warhead weights.
A similar case recently happened when Kheybar-Shikan which is a single skip glide missile for borderline hypersonic MaRV hit at 2100 KM when fired from Yemen to Ben-Gurion airport while IRGC calls it a 1600 KM missile. Fattah-I/II hypersonic missile without Skip Glide trajectory with max altitutde may hit 2500+ KM but with less speed because KE wont be gained without Skip manuvers.
Also western rocket commentators for a long time have been saying that two SLVs in IRGC possession Qassed and Ghaem are ICBMs because instead of ISA (space agency) they are operated by IRGC on mobile TEL. Both are tristaged esp Ghaem is tristaged solid fueled monster with a ISPs matching Russian Yars ICBM. Both have been extensively tested as SLVs.
Possibly K-4 was fired at its max range with 500-700 KG warhead which can travel to 3500 KM.