I understand, but that’s unlikely. If you take a look at the GitHub repository for the extension manager, it will tell you it just “runs composer (sic) under the hood”, and unfortunately InfinityFree doesn’t run Composer server side. This has come up before.
Now weirdly enough I have used the extension manager here successfully in the past, but only for some extensions. I can’t explain it, and it hasn’t worked since. If it’s really a necessity, you may need to upgrade to premium, or rent a VPS so you have complete control over what runs. Flarum is intended to run on a service that has SSH access after all.