The Amp hour rating of the battery only determines how long the inverter will run on a given load.
Whether the inverter can run at full power is determined by the total Amps the battery(s) can produce. For a 6.5KW inverter... I will assume a 94% efficiency. That means at full power the battery needs to provide (6500W/.94)/52V=133A,
Most 48V server rack batteries have BMSs with only 100A discharge capability. Consequently, a single battery would not be able to provide enough current for a continuous 6500W. At about 4.9KW the current draw from the inverter would trip the BMS to shut down. There are a few server rack batteries that have 200A BMSs. A single one of these would be able to handle a 6.5KW inverter at full power.
Some of the wall-mount batteries that are coming out also have 200A BMSs. As an example, the wall-mount battery that EG4 just released has a 200A BMS and could run a 6500W inverter at full load.