Strong lensing offers a precious opportunity for studying the formation and early evolution of super star clusters that are rare in our cosmic backyard. The Sunburst Arc, a lensed Cosmic Noon galaxy, hosts a young super star cluster with escaping Lyman continuum radiation. Analyzing archival Hubble Space Telescope images and emission line data from Very Large Telescope/MUSE and X-shooter, we construct a physical model for the cluster and its surrounding photoionized nebula. We confirm that the cluster is ≲4 Myr old, is extremely massive M
⋆ ∼ 107
M
⊙, and yet has a central component as compact as several parsecs, and we find a gas-phase metallicity Z = (0.22 ± 0.03)Z
⊙. The cluster is surrounded by ≳105
M
⊙ of dense clouds that have been pressurized to P ∼ 109 K cm−3 by perhaps stellar radiation at within 10 pc. These should have large neutral columns N
HI > 1022.8 cm−2 to survive rapid ejection by radiation pressure. The clouds are likely dusty as they show gas-phase depletion of silicon, and may be conducive to secondary star formation if N
HI > 1024 cm−2 or if they sink farther toward the cluster center. Detecting strong [N iii]λ
λ 1750,1752, we infer heavy nitrogen enrichment
log
(
N
/
O
)
=
−
0.21
−
0.11
+
0.10
. This requires efficiently retaining ≳500 M
⊙ of nitrogen in the high-pressure clouds from massive stars heavier than 60 M
⊙ up to 4 Myr. We suggest a physical origin of the high-pressure clouds from partial or complete condensation of slow massive star ejecta, which may have an important implication for the puzzle of multiple stellar populations in globular clusters.