Deeper IR, microwave and radio. Within a galaxy, redshift can be ignored. In another galaxy, the issue is moot, you don’t need to worry about them and they don’t need to worry about you.

Our current scopes can pick up brown dwarfs with a surface temperature below freezing. An object the diameter of a planetary orbit, with the gravitational effect of a main sequence star and giving off just black body radiation is gonna stick out like a neon “Interesting stuff here!” sign the moment someone does a long wavelength survey of your general region.

Even if you build a swarm instead of a solid shell, you’re still going to shift the star’s apparent spectrum towards IR, from the swarm radiating waste heat. A star whose mass, diameter and emission spectrum don’t match up with the math is inviting investigation, regardless of how you try to mask what you’ve been doing.

I would think it’d make it more likely that you’re discovered when you turn your star into a black ball with a gigantic IR signature where a star should be. Any civilization with a cursory understanding of gravity and stellar spectra would turn every telescope they have on you.