What’s the difference between using the company/organization webmail client vs email client on your own (Thunderbird/K-9)? What kind of data do I avoid of being collected when I use my own email client instead of using the email provider webmail client?
It should be the same.
Its safe to assume that Google scans GMail message content as it arrives. Opening it on whatever client you want has no effect on it. I think the potential difference only has an effect if your account is part of GSuite or not. They claim they dont do analytics on GSuite accounts, but there is no way for us to tell.
It should be the same on all free email providers.
Regarding Thunderbird and K9, it should be reasonably the same. For local email clients, at least no ads are shown. Some email providers dont allow this on their free tier (Yahoo! comes to mind).