We report the flexible on-target delivery of 800 nm wavelength, 5 GW peak power, 40 fs duration laser pulses through an evacuated and tightly coiled 10 m long hollow-core nested anti-resonant fiber by positively chirping the input pulses to compensate for the anomalous dispersion of the fiber. Near-transform-limited output pulses with high beam quality and a guided peak intensity of 3 PW/cm² were achieved by suppressing plasma effects in the residual gas by pre-pumping the fiber with laser pulses after evacuation. This appears to cause a long-term removal of molecules from the fiber core. Identifying the fluence at the fiber core-wall interface as the damage origin, we scaled the coupled energy to 2.1 mJ using a short piece of larger-core fiber to obtain 20 GW at the fiber output. This scheme can pave the way towards the integration of anti-resonant fibers in mJ-level nonlinear optical experiments and laser-source development.