Do not assume it pauses or extends the deadline. Address the actual notice promptly through the responsible process.
Assign responsibility before the transition
Keep the due date and required response clear. Neither a change of adviser nor a contact-update request guarantees extra time, approval or permission to move.
The current official FAQ says the process should take weeks after the processing fee and application are received, assuming timely documents and interview attendance, but that is not a guaranteed deadline. Keep deadlines from government communications visible and provide accurate requested material through the proper process. Deadlines belong to processes, and the process with the nearest deadline governs your next action regardless of which project matters more. Official material describes the process in terms of weeks, but that is a description rather than a commitment, and vetting, visa availability, an interview, or a further document request can each extend it. Payment is a step in the published process; permission to enter, live or work comes from the immigrant category a successful applicant proceeds through, subject to its eligibility rules, admissibility and visa availability. Do not assume a private preparation delay changes an official date or that a generic package guarantees a favourable decision. The actual effect on timing depends on the facts and requests; no fixed delay or approval date can be promised.