Accessing, sharing, and managing documents and media within Microsoft Teams Free
Hello,
Unfortunately this is not something you can fix on your end. I will explain -
The other user you work with is an organization user, so joining their meeting or access their files are regulated by their organization's group policies set by their organization IT (not Microsoft).
In your case, it shows that their IT didn't enable the policy to allow their users to collaborate with unmanaged users (aka personal microsoft account users) in their Teams Admin Center. It is up to their IT to determine if they would change this policy for their organization.
However, for the time being, you can continue joining meeting via the web without signing in. And to access the file sharing, tell the meeting organizer to download the recording to their own OneDrive folder, then right click to share the file, and choose "anyone with the link" option, copy the link and send you the link directly. Tell them not to email you on the "share" pop up.