This doesn't pass the smell test. For constant light the satellites would need to be in something like geosynchronous orbits, which is "very far away"(tm). Closer in and you'd need Starlink 2.0 quantities to get coverage.
Even then, the size of the orbiting reflector would need to be absolutely gargantuan to reflect enough sunlight to be useful.
Even then, the size of the orbiting reflector would need to be absolutely gargantuan to reflect enough sunlight to be useful.