Uploads stuck or slow
Uploads run as WordPress background tasks. If they aren't moving, WP-Cron is probably off or being blocked, and Offloft shows "Background tasks aren't running". Click Run now to process what's waiting, and add a real cron job so they keep running. Your site keeps working from local files meanwhile.
WP-Cron is off
If DISABLE_WP_CRON is set, your server has to run it. Settings → Advanced shows the crontab line for your site.
Your host blocks background requests
Offloft may say your host is blocking WordPress's background requests. Run now processes them, and a real cron job avoids the problem. From WP-CLI, wp offloft run processes the tasks due now.
Check the job
Jobs shows whether a job is running or paused. A paused job resumes from there. A provider outage pauses work too, and it continues by itself.
Slow rather than stuck
The speed depends on your host. Work runs in small batches by default, and the limits in Settings → Advanced can be changed if support asks. Start with the defaults: 4 uploads at once is safe on shared hosting.