  Tenuous wind bubbles, which are formed by the spin-down activity of central
compact remnants, are relevant in some models of fast radio bursts (FRBs) and
super-luminous supernovae. We study their high-energy signatures, focusing on
the role of pair-enriched bubbles produced by young magnetars, rapidly-rotating
neutron stars, and magnetized white dwarfs. (i) First, we study the nebular
properties and the conditions allowing for escape of high-energy gamma-rays and
radio waves, showing that their escape is possible for nebulae with ages of
>10-100 yr. In the rapidly-rotating neutron star scenario, we find that radio
emission from the quasi-steady nebula itself may be bright enough to be
detected especially at sub-mm frequencies, which is relevant as a possible
counterpart of pulsar-driven SNe and FRBs. (ii) Second, we consider the fate of
bursting emission in the nebulae. We suggest that an impulsive burst may lead
to a highly relativistic flow, which would interact with the nebula. If the
shocked nebula is still relativistic, pre-existing non-thermal particles in the
nebula can be significantly boosted by the forward shock, leading to
short-duration (maybe millisecond or longer) high-energy gamma-ray flashes.
Possible dissipation at the reverse shock may also lead to gamma-ray emission.
(iii) After such flares, interactions with the baryonic ejecta may lead to
afterglow emission with a duration of days to weeks. In the magnetar scenario,
this burst-in-bubble model leads to the expectation that nearby (<10-100 Mpc)
high-energy gamma-ray flashes may be detected by HAWC and CTA, and the
subsequent afterglow emission may be seen by radio telescopes such as VLA. (iv)
Finally, we discuss several implications specific to FRBs, including
constraints on the emission regions and limits on soft gamma-ray counterparts.
