Do not let the pending permanent-residence plan obscure an actual temporary-status issue. Obtain a timely assessment of the relevant records and options.
Use the deadline from the correct process
This page does not determine an individual deadline or prescribe a filing. The important planning step is to identify what governs the present stay and work while the separate Gold Card outcome remains unresolved. Deadlines belong to processes, and the process with the nearest deadline governs your next action regardless of which project matters more.
Identify the temporary assignment's dates first, since they are usually the ones that expire, and treat the permanent-residence track as something scheduled around them rather than the reverse. Note also that the two tracks can interact in ways worth asking about specifically, particularly around travel, a change of employer, and any period when one status has ended before another begins. Those are questions for counsel, put in advance, not conclusions to reach alone.
What goes wrong is waiting: a date approaches, the household assumes the other process will resolve first, and the options that existed a month earlier are gone. Ask early enough that doing nothing is still a choice rather than an outcome.