Send files between two tenant

And why would you even want this? This is what external collaboration is for! 😁

This is completely frustrating. "designed to keep your data safe." MSFT says...I think we should be able to decide what we wish to share. Period

If the other organization is an organization you ”trust” and collaborate a lot with,  Multitenant Organization gives you a better experience when it comes to ”Private chat”, BUT it requires good planning and you need to ensure that both tenants are configured/secured as they ought to be. You can read more about that here: https://learn.microsoft.com/en-us/microsoft-365/enterprise/plan-multi-tenant-org-overview?view=o365-worldwide&WT.mc_id=email&sharingId=M365-MVP-5005370

However, the easiest way to solve your need is to use a team and channel posts/files with people from the other organization as guests.

Just adding to what VasilMichev has rightly pointed out - the other option would be to use the 'share' function in SharePoint or OneDrive and paste the link into the chat (or send it via email)

Teams does not use file transfers, but file "sharing". In other words, it relies on OneDrive for Business for this functionality. And it's not available in federated/external chat scenarios as detailed for example here: https://learn.microsoft.com/en-us/MicrosoftTeams/communicate-with-users-from-other-organizations#compare-external-access-and-guest-access