These caps are set by each CRM platform, not by Lusha. If your selection exceeds a CRM’s cap, Lusha exports the first N contacts and leaves the rest marked Not exported - so your next run picks up exactly where this one stopped. Only one export can run at a time per user.
Async export beyond the real-time threshold is available for contacts and companies on Salesforce and HubSpot. On every other CRM listed above, company exports are limited to the real-time threshold and cannot run as a background/async job.